Get a t3i because 720/60p and manual exposure controls.
Use the Kit lens from that for followcams. 18mm is plenty wide. Shoot at f11 or more, since you're on bright ass snow, and you need to keep your subject in focus anyways. Pick up a polarizing filter. You'll have some distortion from the Kit lens, but it's really not bad, especially for learning - which you are.
Don't drop 500+ on the Tokina 11-16. Only get it if you're REALLY going to get close in there on your subject, or if you're filming when there's limited light out. You don't need much wider than 17mm for the gran majority of your shots.
Have a nice day, Bluename.