An air cast is a bit drastic, considering that he's not playing sports or anything, but I suppose with the snow and all it could help...
Teir, an air cast is a somewhat hard "cast" that's solid on the sides and open in the front and back that wraps around your ankle/lower calf, stabilizing the ankle and preventing it from "rolling". They're available at your local Rite-Aid/Duane Reade. The reason you've had the same injury to the same foot twice is because when the ligaments become stretched/torn, it leaves you more prone to roll the same ankle again, since there's less support/stabilization on the joint.
I've sprained many an ankle in my day while playing basketball, and I remember that it took almost 2 years without a "roll" (i.e., a sprain) for my ankle to be as strong as it was before the sprains; I could tell it was still weak because when I would be walking down the street and there was a twig on the ground or a small dimple in the concrete, my ankle would just give out sometimes and I'd end up hurting it (not terribly, but it'd roll). After an ankle sprain, always be careful of where you're stepping in order to prevent an inadvertent roll. Ice and elevation is good for the first day or so to contain swelling, but don't ice it for a prolonged period of time.
As long as the swelling isn't too bad and it doesn't turn black and blue or anything, you're pretty safe with not seeing a doctor. Just wait it out and it'll heal eventually. Depending on the severity of the sprain, however, it may take up to a few months. The worst sprain I ever experienced took about 4-5 months to heal fully, but that was from playing ball and landing from a jump, so the pressure was much greater. Still, be patient with it and be careful.
