I an making a medieval society that uses a wolf-like animal as steeds instead of horses (in case it helps to have a description, think of a wolf built like a deer) and I wanted to know if it could out-run a horse within a hundred meters of each other.
Realistically? No. Horses have skinny limbs for a reason... so there's less weight to move as their legs go back and forth, and really hefty muscles at the base of each. A horse will outrun the wolf, but their weaker limbs (limbs themselves, not the base) will make it hard to struggle if wolves surround them (as wolves generally try to do.)
Unless, of course, the horse is weak for some reason. (Already exerted, tired, old, young, etc.)
The wolf would lose in a sprint, but could chase it down over a marathon.
Horses have skinny legs and bodies designed for fast bursts. They need a lot of energy to keep going, and they get exhausted quickly.
By contrast, wolves are designed for stamina. They hunt down their prey in packs over long distance. As soon the prey gets tired, the wolves close the distance.
The horsemen would leave the wolf cavalry behind at first. But then the horses tire (especially when carrying a rider) while the wolves keep going for a lot longer.
You'll probably find that at the same size they're about the same speed.
The smaller animals have more acceleration, the larger ones more endurance. The good old square cube rules come into play again, being taller gives you more stride length, but also more mass, that makes you slower to accelerate.
The bigger problem is feeding them. Larger predators need larger prey, a pack of wolves the size of horses will need to bring down a couple of elephants a week to survive. The largest wolves currently are the Canadian timber wolves and they mostly hunt bison, they need to be larger as a result of the size of their prey but there are still limiting factors.
A horse runs about 70km/h when super speed and 50km/h when 'normal' gallop
The wolf can run about 50-60 km/h according to google.
A wolf is about 1m high, that means it grow about 50-100% due to this question.
With simple math the wolf could run 75km/h to 120km/h. (unrealistic)
To calculate realistic the legs of the wolf need to get stronger, with that the legs are getting heavier as well as the whole body. The acceleration drops hard and the top speed too. I would estimate the wolf be faster as the horse, but definitely not above 100km/h
I hope this helps
Ligers have a carnivore body plan and at 10 feet long and 750lbs will stand in for your horse sized wolf. According to this liger enthusiast site, ligers can run 60 mph - twice as fast as a horse.
A liger is capable of gaining a speed momentum of around 50 to 60 miles per hour. This 50 to 60 miles per hour speed for a a liger, allows it to be faster than lions and equally faster to the tigers. Furthermore; ligers with this speed are only at the second spot just behind the Cheetahs which are capable of speeding around 70 miles per hour. Dr. Bhagavan Antle is measuring the speed of ligers for many decades at its Animal Preserve (The Institute of Greatly Endangered and Rare Species T.I.G.E.R.S.). He has witnessed the speed of 60 miles per hour from a liger named as Sudan the liger and also an average of 50 miles per hour speed from his other ligers as well.
But somehow I don't see big boy here keeping that kind of speed up for very long.
Wolves can run down a horse
Wolves hunt and kill caribou regularly. In that video, a single wolf chases down (and kills a caribou). A caribou's top speed is 60-80 km/h according to Ultimate Ungulate, a source I am partial to. Guinness says the highest speed ever achieved by a racehorse is 70 km/h.
Therefore, if wolves are designed to chase down caribou, and caribou are roughly as fast as horses, it is reasonable for a wolf to chase down a horse.
If the wolf is 4 times larger, then that is even more reason for the wolf to win a footrace.
If you change the wolf's body a bit more then just his size ( with what I mean on his weight ) they could go faster over long distances but not necessarily in a short sprint. It's your world so you can give them more stamina ( and lighter body weight, because as I understand no one said that you must make them muscular and ), increase time that they can run before they get hungry and make them more "puffy" then mad stone muscle. Something like if you tried to make a werewolf.