tl;dr: Green houses and/or hardy plants.
Note: When I first answered, I missed your mention of Celsius. I was thinking -5 to 10 degrees F, which is even colder. This realization makes what you want even easier. There are edible garden plants which can survive the temperature range you specify just fine. I have edited the answer with this updated point of view. Sorry if my changes cause any confusion.
Some people do maintain gardens through the winter. You just need a hardy plant and to help it along. Your people could grow kale in small greenhouses. A horizontal window is all you really need for this, or even just a layer of normal clear plastic-wrap used on left-over food. A window can even be propped up by the snow itself. All you need to do is keep this small space above freezing. With the right plants, even if it gets below freezing they won't necessarily die. Keeping it almost always above freezing also provides the added benefit that you now have a good source of water too, for both you and the plant; just toss snow in there and let it melt.
Do a Google search for winter gardening advice. I typically do one like "Best crops for winter garden". Lots of the articles will just suggest lists of plants and how to care for them, but some actually specify temperature ranges below which you should expect the plants to die.
For example, at growveg.com Best Vegetables to Grow in Winter, we see:
But I have learned this truth about growing winter vegetables the hard
way: Grow only as much as you can protect from the elements, because
that's the essence of the task. Where I live, winter temperatures
occasionally drop below 0°F (-18°C), with several significant snows
and winds that howl for days at a time. Spinach resting in a cold
frame with a tempered glass lid (made from an old shower door)
scarcely know what's happening, and the same goes for onions snug
inside a sturdy tunnel covered with heavy-duty row cover (garden
fleece) and an old quilt.
And from Aggie Horticulture, Texas AgriLife Extension Service, Texas A&M System:
In general, a frost (31-33 degrees F.) will kill beans, cantaloupe,
corn, cucumbers, eggplant, okra, peas, pepper, potatoes, sweet
potatoes, squash, tomatoes, and watermelon.
Colder temperatures (26-31 degrees F.) may burn foliage but will not
kill broccoli, cabbage, cauliflower, chard, lettuce, mustard, onion,
radish, and turnip.
The real cold weather champs are beets, Brussels sprouts, carrots,
collards, kale, parsley, and spinach.
26 degrees F = -3 degrees C. Assuming the "cold weather champs" listed above will fare better than the ones in its previous paragraph, that provides a small list of crops that should survive even at -5 C *without any special greenhouse or other intervention." So, with a simple greenhouse, or better, you should be able to keep some of your crops alive even below -5 C, possibly even down to -20C or -30C, more if you provide enough heat inside it.
Note that even if a plant does not die that does not necessarily mean that it is still growing, or growing well, at a given temperature. If you grow kale, even if it does not die at -5C it might not grow a reasonable amount until the temperature gets back up to 5-10C or until you warm it.
If you design this with solar heaters, it will be even easier and warmer.
If your temperature gets down below -5C a lot and your diet is primarily plant based, then you will need to cover a lot of land like this. The amount might seem infeasible to you or I, but if it is necessary to survive then people will do it.
It could be difficult but not impossible. If I were given 1 roll of food plastic-wrap in an environment like you specified, I could probably cover enough kale to keep me going for a long time.
I think people often underestimate the effect a simple window can have. When we go out in the winter and get into our car on a very cold day, it still feels very cold in the car but what you might not realize is it's still much warmer than outside the car, assuming the windows are not covered by snow or other impediment. If a car is properly oriented to maximize sun exposure to the windows, it can be below freezing out but warm enough in the car to not need a coat.
A properly designed greenhouse with all the best fixtures, such as multi-pane glass, good light-absorbing material inside to maximize the heating, and circled by passive solar heaters, could easily raise your temperatures a lot.
Source of information note cited: Experience. I have melted snow in ways similar to this specifically to get water from it. I have friends who grow kale through the winter. Usually at least three to four months of the year where I am is much colder than you specify; we consider it a warm day if it reaches the mid-point in your range. Also, I have made a solar heater using nothing but plastic wrap, cardboard, duct-tape, the screen from a door, and a little bit of wood, and even a small crude device like I made noticeably raises the temperature inside it.
If you want a more fantastical, outside-the-box approach, you could suggest that cold-weather trees are so prevalent in your area that people are wasteful with their wood use. People burn long-term fires which rage for months at a time and provide enough heat to grow crops.
This practice does not need to be sustainable, perhaps a note in your story that this is a new practice which is deforesting the area, but this is the time that the story is set in. Or maybe it is sustainable because you have either abnormally fast growing trees or very few people.