heaters can be bad and turn out with REALLY bad results as they are dangerous for a rabbits to go near. get him a dog bed with blankets and on cold days and nights but in a hot water bottle under the blankets they usually love this in the cold several of my rabbits have.

Your rabbit will be fine as long as he isn’t in any direct drafts. Rabbits love cold weather. The thing that is bad is if they get wet and sit in a draft. they can then get a respitory infection and that can turn nasty.
Give him a wooden box filled with hay and he can then make a burrow to sleep in. Make sure you check the water so it doesn’t freeze.
if his cage sits diretly on the floor you can raise it up to keep the cold off of the bottom of the cage.

i have raised rabbits for 16 years and all of mine live in an unheated garage. The temps here in Ohio can get down to zero. My rabbits do fine and always have.

Rabbits are designed to live through winters. They grow extra fur. Get a blanket or a dog sleeping thing. Build it a box and put some old shirts or things. Hope I helped!

My bunny thumper lives in the garage and we keep a heater in there but he never really needs it cuz of all the fur and heaters are expensive if you dont own one so i sugest giving him an old towel or blanket to cuddle up with. if he chews it thats fine but if he pees on it then chews it trow it away cuz rabbits eating there own pee is unhealthy and can cause liver damage.

Even with all that fur they still get cold easy. Make sure he is where there is no cool air coming in. Make sure he has lots of nice fresh hay where he can snuggle into. Blankets are good to as long as he is not a chewer. If he is (like mine) this is not good. Another good thing you can do is cover his cage up with a blanket. Not real heavy one ,but one that will keep his body heat in. Make sure you do leave some of the cage exposed for air to come in. When the sun comes out during the day let him hop around again if he is like mine. He will soak up that nice warm sun. Even though its cool make sure he has water and food. He should be fine.

Get a small heater to put in that room to keep it at a good temp, Tons of polar fleece blankets will help to. And its great because polar fleece will not fray if he chews it a little. Hay is also a good insulator so a big box of hay he can climb inside will give him a nice warm get-away. Plus moving him away from the windows to keep the draft off of him.