how is the 11-16 a good all around lens? it's literally the opposite, but that's irrelevant.
apart from what has already been suggested, i'd recommend looking into the nikon 16-85. you can probably find it for about $500 and it's extremely sharp and versatile. it's a little slower than the tamron 17-50, but i wouldn't worry about that at all for filming skiing. it also has a better range, far superior optics, good build quality, and a VR system that actually works. if you look up this lens you will see i'm not the only one raving about it