It seems to me that the X5 and X6 are identical in virtually every way other than the exterior sheet metal (and, of course, the resulting decrease in interior space). Therefore, I don't see how the X6 would perform any differently than the X5 in the snow or otherwise.

The X6 is certainly a bit smaller on the interior. If you like the X5's room, stick with it. If you're curious about whether the X6 would work for you, go to your dealer and ask if you can test drive an X6 for a couple of days. If they won't let you, pack up your X5 as you normally would for an "outing," drive to the dealer, and then ask for a test drive in an X6 with all your kit loaded up in it. That should give you the best idea of "space" you're bound to get short of owning the thing.