Why is everyone saying the 50L isn't good for video? Of course none of the DSLR lenses are technically good for video (except Zeiss stuff), but I've gotten some absolutely stunning footage with my 50L. I rarely shoot below f/2 with it, but it's sharpness, contrast, and bokeh look friggin amazing on stills or video, if you can say it's not good for video you're saying it's not good for stills.
But OP I agree with some of the others that the 7D may not be the ideal camera for what you're trying to do, it suffers from rolling shutter artifacts pretty badly and if you're going to be doing whip pans of skiers passing by you're going to end up with a whole bunch of unusable footage, and there isn't really any way around that. There are plenty of other alternatives out there nowadays, I'd seriously consider something else before dumping anymore money into it. DSLR's are great for some stuff, like shooting in a fixed studio environment, but for what you're describing I think they are a poor choice.
If you do insist on sticking with a DSLR, I think the 70-200mm will feel much too long on a 7D, no way you'll be able to get steady footage outside of shooting on a tripod. I think the 35L would be a better choice if going with primes, as even 50mm is pretty long on a 7D.
I think you need an ultra-wide for sure, you can get lots of great landscape shots and some dramatic closeups of skiers. For $2300 I'd suggest:
- Tokina 11-16mm- around $600 and super wide on a 7D
- Canon 17-55mm f2.8 IS - $800-900 used
-Canon 70-200 f/4 - $700
You'd have a long range covered and be able to do quite a bit of stuff with those lenses. I think if you're constantly shooting outside you probably don't want to have to deal with primes and switching lenses all the time, these lenses will give you some flexibility.
Now I don't know if that budget was supposed to include accessories too, but you're going to need some other stuff outside of lenses. A shoulder rig of some sort, possible a steadicam for shooting while skiing, tripod, monitor or evf, etc.