The character would probably die almost instantly.
The original question asks:
The human must be able to walk and pull a cart containing these foods for 2 years in a Mars-like environment.
Everything that people have suspected about a Mars-like environment in the 20th century, and all they have learned about a Mars-like environment since 1964, says that the atmosphere of Mars has only a tiny fraction of the atmospehric pressure necessary to maintain human life.
A person would loose conssciousness and suffer fatal injuries with seconds of exposure to the Martian atmosphere, or even an atmosphere which was several times as dense as the Martian atmopshere. And the Martian atmosphere has only trace amounts of oxygen, so if it was concentrated to the same pressure as Earth's atmosphere, someone would still suffocate quickly when breathing it.
No environment which is even remotely Mars-like can be survivable for an unprotected human.
So maybe the human is not unprotected. Maybe they wear a full spacesuit when they pull their cart around on the Mars-like surface.
That means that a lot of the space and weight capacity of the cart would have to be used to extract oxygen from the Martian atmosphere or soil somehow to replenish the oxygen supply of the person's spacesuit, and the power source for the oxygen device.
That leaves a lot less room for food in the cart. I believe that I eat several pounds of food and water each week. So for about 2 years or about 100 weeks someone would need a load of several hundred pounds of food and water to carry around in their cart.
So how does the space suit wearing human actually eat and drink the food and water they pull around in their cart? How does the food and water get from outside the spacesuit to inside the spacesuit without the human losing air and dying? And how do they excreate while wearing the spacesuit?
It would be a lot more plausible if the human lived in a pressurized habitat where they didn't have to wear the space suit, and only went on long trips outside the pressurized habitat pulling the cart when they had missions requiring them to be out of the habitat for several days at a time.
I note that in a spaceship or a large habitat in space or on a planet, an advanced enough technology would enable the recycling of all waste products via complex chemical reactions powered by a powerful energy source into breathable air, drinkable water, and nourishing foods.
And possibly after such recycling becomes common in space ships and large habitats, centuries of improvement and advances will enable such recycling equiment and its power source to be miniaturized small enough to be built into a spacesuit, so that someone could survive in a spacesuit for months or years without ever taking it off.
And possibly before that recycling equipment becomes miniaturized enough to be used in a spacesuit, a slightly less miniaturized version would become available which could be installed in a cart pulled by a human in a spacesuit with various umbilical hoses connecting the cart and the spacesuit, so that the cart is effectively a vital part of the spacesuit.
But in that case the recycling system would synthasize air, water, and nutritious foods for the human, and they would not need to carry hundreds of pounds of air, water, and canned(?) food with them in the cart.
As I wrote, any environment which is "Mars-like" would be almost instantly lethal for a human without the protection of a pressurized habitat or a spacesuit.
But possibly the question means an environment with Mars-like gravity for making pulling a cart loaded with years of food in it easier, but with an Earth-like atmosphere which is breathable for humans. Thus the human wouldn't need a spacesuit, heavy oxygen bottles, or a device to extract and concentrate oxygen from the atmosphere or the ground.
And so they might not have devices to recycle wastes into synthasized food, and thus might need to rely on canned(?) food and water supplies which they have to pull behind them in a cart.
But is a planet with low, Mars-like gravity and a breathable atmosphere possible?
The important atributes to consider here are the surface gravity of a planet and its escape velocity.
The surface gravity of the planet should be low enough that movement and pulling heavy loads is much easier than on Earth, while high enough to avoid problems with movement and avoid the long term bad health effects of microbravity.
And the escape velocity of the planet has to be high enough to prevent oxygen and other necessary gases from escaping.
The surface gravity of a planet can be calculated from the equations here:
And the escape velocity of a planet can be calculated from the equations here:
And I have noted that for planets, moons, and other objects less massive than Earth, the listed surface gravity decreases faster with a decrease in mass than the escape velocity does, so that the escape velocities of those smaller bodies are higher, proportional to Earth's escape velocity, than their surface gravities are proportional to Earth's surface gravity.
Which helps a bit in having planets with lower surface gravity retain their atmospheres.
There is an estimate about how small a planet could be and still have an atmosphere breathable for humans.
Habitable Planets for Man Stephen H. Dole, 1964, 2007, is a scientific study of the requirements for a planet to be habitable for humans.
Pages 13-19 discuss the atmospheric requirements, and pages 53 to 58 discuss the mass requirements for a planet to retain a breathable atmosphere for geological amounts of time.
On page 54 Dole calculates that the minimum escape velocity for a planet to retain a breathable atmosphere is 6.25 kilometers per second, corresponding to a mass of 0.195 Earth and a surface gravity of 0.49 Earth. But Dole believed such a planet would be too small to produce enough oxygen for humans to breath.
Dole made two different estimates of the minimum mass of a planet that could produce an oxygen rich atmosphere, 0.25 Earth and 0.57 Earth. Dole decided that the correct minimum mass should be between those figures, and thus about 0.4 times the mass of Earth, which corresponds to a planet with a radius of 0.78 Earth radius and a surface gravity of 0.68 Earth.
However, discoveries since Dole wrote indicate that it might, repreat might, be possible for a world with lower surface gravity than that to have a breathable atmosphere.
Titan, the largest moon of Saturn, has a very surprisingly dense atmosphere considering its low surface gravity & escape velocity. Its surface gravity is only 0.36 that of Mars, while its escape velocity is only 0.52 That of Mars. But Titan has an atmosphere many times as dense as that of Mars.
In fact, Titan's atmosphere has a atmopshere 1.45 times as dense as Earth's, despite Titan having a surface gravity 0.137 that of Earth and an escape velocity 0.235 that of Earth.
So perhaps it is possible for a planet to have a surface gravity like that of Mars, temperatures similar to those on Earth, and a breathable atmosphere.
However, part of the reason that Titan has a dense atmosphere is because it is so far from the Sun, and way too cold for unprotected humans to survive. Humans would need very warm clothing to survive on Titan. And while Earth's atmosphere is about 78 % nitrogen and 20.9 % oxygen, Titan's atmosphere is about 97 % Nitrogen and 2.7 % methane, with no oxygen detected. So humans would have to use breathing apparatus on Titan.
Titan offers hope that a planet with Mars-like surface gravity and Earth-like temperatures might have a breathable atmosphere, but not proof that is possible.
Another possibility might be a story set in a vast artificial space habitat, a hollow cylinder which rotates to provide Earthlike gravity.
So perhaps a vast cylindrical space hapibtat has been constructed and has been supplied with an atmosphere, and is being slowly spun to provide Earth-like gravity for the eventual settlers.
But it will take years or decades to get the vast mass spinning fast enough to avoid long term health problems for the settlers, so the station is deserted at the moment.
But maybe two people have snuck into the station to fly with artifical wings attached to their limbs, which is practical near the center axis of a rotating space habitat but not near the surface where the gravity is too high. Inside this station the gravity is not yet too high at the surface for human powered flight, so they can land and take off from the inner surface, which they couldn't do in a habitat ready for occupation.
So maybe the two people are flying low over the surface and can easily land when they want to, unlike in an inhabited habitat, when suddenly some interior storm strikes them and scatters them. They land separately too far apart for each to see or guess where the other has landed, and the protagonist's wings are broken beyong repair.
But the station has a hundred levels of interior space below the inner surface they were flying around above. Those levels wiil be interior spaces for people to live in and for all the food synthiszers and other life suppport equipement which will be installedin the future. The surface area will be reserved for parks and other recreational purposes.
Those lower levels were built in many thousands of airtight segments that were joined together to form the giant cylinder. And the airtight airlock doors between each segment are locked and won't be unlocked until the station is made ready for habitation.
And the protagonist knows that there are emergency supplies in each segment for workers who might be stranded due to accidents.
So he opens a door to a ramp down into the lower levels, and finds the emergency cache, which is in the same location in every one of the shousands of segements. He finds a cart and loads it up with all the water and food he can pull in the very light gravity, leaves a note for anyone who might happen to come there, and pulls the cart back up the ramps to the inner surface of the cylinder.
And then he sets out across the inner surface until he reaches one of the ends of the cylinder. Then he pulls the cart up ramp after ramp after ramp, the elevators probably not being powered yet, up kilometers to the central axis of the habitat, where their space ship is parked. His partner isn't there.
He waits for the partner as long as he can stand to, and then leaves a note at the spaceship and returns to the inner surface of the cylinder. And then he searches the inner surface of the cylinder for his partner who could be dead or injured, and goes down to the emergency supply place in each seqment, checks to see if any supplies have been taken, and leaves a note for anyone who might find it.
And it may take him years to search the entire habitat, replenishing his supplies from the emergency supply places, until he either finds his partner or the work crews arrive to begin readying the habitat for the colonists.
And this is the best I can think of to justify someone pulling a cart loaded with food and water through a "Mars-like" enviroment.