My donkey is suppose to be from mammoth stock but is only a large standard size of 13 hands. He hates being stalled and will chew the barn down! My stalls will never be the same after he was in them. LOL. In the winter he is outside with the horses and a run-in shed. The big thing is to have a dry place they can go to get out of the wind. They hate wind in their long ears.
When we do get snow it doesn't seem to bug him. He HATES mud but deals with it when we have wet weather. Its just funny because the horses will cut straight through but he will go around the long way to avoid as much mud as possible.