I can't believe noone answered this....
The answer is yes. DEFINATELY!!! I live in northern Maine (USA) and there are many weeks in the deep dark winter that it can reach -20 to -40. and tons of folks raise chickens, rabbits and many many other small livestock animals here.
Rabbits are a great winter animal, they put on extra fur in the winter that helps them keep warm. when raising rabbits in cold climates there are a few tricks though.
1. keep a good supply of unfrozen water available (not arm water, just unfrozen) I use heavy ceramic bowls in the winter and change them 3 or 4 times a day. but there are many "heated" watering systems available.
2. when using wire cages (which are prefered over hutches) make sure the rabbit has a place to sit that is off the wire. I use a square of 1/4 inch plywood that covers about 1/4 of the cage floor.
3. It is VERY important that the animal be kept out of the wind. an airtight building isnt necessary and may be detrimental to a rabbits health in most cases, but a draft can be deadly at colder temperatures.
4 don't breed your raqbbits in the winter if you are not heating the "rabbit house" the stress is too much for the doe, and most babies will be eaten by a stressed mother.
5. if you know you are going to have an extraordinary cold spell, add some straw to the cages the rabbits will nest in it and do just fine.
as far as chickens... the water rule applies to them as well.
unlike rabbits, chickens don't know much abot nesting so the best thing to do is build them a small, well insulated coop with a heated water source. and put them all in the same space. I have my chickens in a 8ft by 8ft insulated room in the barn and last winter i went in there and it was 12 degrees inside and 30 below outside...the chicken all lived through the cold winter just fine.
by the way 18 chickens wintered in that room.
I hope this helps you and others. and good luck.