I'd vote on the two-lens combo, something wide (17 to X-ish) and something tele (70 to X-ish). I would definitely skip the crazy-range zoom (17 to 200-ish) unless you're more concerned with continuous range than image quality.
But it really depends on what you want to do.
I shoot professionally for editorial publication (and video for online)-- but primarily not skiing. I use a 35mm f/1.4 lens for 80% of my work, followed by a 17mm f/3.5 and a 135mm f/2. Got a couple random lenses that I don't use very often (manual: 24mm f/2.8 and 55mm f/1.2).
The best generic advice I can give is: MOVE CLOSER. A wide lens, and close to the subject, provides a lot of feeling. Tele and distance tend to create flatter, more distanced (big surprise) images. But it all depends on what you're after.
Definitely go ahead and get the kit lens that comes with Canon bodies-- an 18-55 IS. It's not the best, but it's actually a useful range, it's image stabilized, and for skiing you'll have plenty of light to stop it down. And its cheap, small, and light. You won't feel bad when you break it.
You might consider using that for a few weeks to figure out how you like to shoot (which end, what kind of images), before investing in more glass. Another wise choice is the 50mm f/1.8, which is foolishly sharp, cheap ($65 used, $100 new), and light. Also not real hardy, but whatever. That will give you a taste of what shooting a prime is like.
The tele lenses in the 70 to 200 range (and the Canon F/4 non-IS is a real winner for price/performance) are relatively big and heavy. I wouldn't want to ski with one in my bag unless I had a real reason to do so (like longish video sequences, or certain jumping/close-in detail sequences in stills or video).
Also, keep in mind that the "effective" focal length of any of those lenses on a non-full 35mm body (anything below a 5D) is actually 1.6 x longer than the lens is listed at. So, that 20mm lens is more like a 32mm lens on film (or full frame digital), and that 200mm lens is more like a 320mm lens. (If you really want to be accurate-- unless we're talking about enlargement and printing-- you're not actually making the lenses longer... you're cropping the center part of the image).
As for a protective filter... nah. Lens glass is very hard/hardy, and protective filters (even really nice ones, which cost around $100) reduce image quality and introduce image artifacts like glare, ghosting, and lower contrast. You might want a circular-pol, but you can wait to add that to your kit down the line.