Not sure about CGs, but winter camping in RMNP is kind of a free-for-all. Check with the rangers' office to make sure they still have that policy. A good camping spot if you don't mind lugging some stuff uphill is near where the trail from Glacier Gorge TH forks to become the "Glacier Gorge" trail (right) and the "Sprague" trail (left). You might even find a platform already leveled there from previous climbers/skiers. If you can navigate lots of deadfall from a storm earlier in the year, the trail to Black Lake from here is nice in winter and only crosses slide zones when slide danger is Very High or Extreme. Realistically, in "extreme" conditions, you really don't want to be out in RMNP anywhere, so keep checking the CAIC website or hotline as you get close to Colo.
Another great snowshoe/ski is the Lake Helene classic ski tour. You can snowshoe it if you must. This departs from the Bear Lake TH, just uphill from Glacier Gorge TH. Once you get to the open treeless section on the flank of Flattop Mtn, however, you might be on your own as far as routefinding is concerned, depending on recent snowfall and the schedules of skiers.
Also from Glacier Gorge, the Loch is a nice place to visit, and provides access to all kinds of travel lines you may or may not be comfortable with, depending on snow conditions.
The Wild Basin TH provides a dearth of low-angle tree travel if there's enough snow for it.
I guess I could go on and on. PM me if you want more info. Also, SP is crawling with RMNP nuts so you'll get a lot more replies to this, I assume. There's a lifetime of exploration waiting for you up in there--especially in winter.
As far as avy conditions are concerned, just keep checking CAIC and, if you don't know how to "see" avalanche terrain or traps, just find and ask a ranger about your next few days' plans--they're very, very conservative with their advice.