I played basketball for my high school and have sprained my ankle many times. Some severe, some not. The treatment was always the same though...REST. One severe sprains, its recommended that you go see a doctor and get an XRAY on it to make sure there is no fracture.
You have mobility so youre past that part. About strengthening and getting mobility back, there are a couple of things you can do.
First off, stand up and balance yourself on that one injured ankle. This will help strengthen your ankle and regain balance on it. This was the best thing I did, and continue to do for my injured ankle.
Secondly, take your hand and rotate your foot both clockwise and counter clockwise slowly.
Lastly, wear a brace when you go out on the mountain. Its going to help stablize it a little.
Hope this helps. Remember to do 1 & 2 everyday in the morning.