Well, you may have to wait till you are on the road to decide!  (That is one of the best aspects of RV travel -- much less need to make firm reservations.)  One year, we were planning to hit the North Cascades in Washington (right on the BC border) in late June, when the trails are usually open.  We called the ranger, who said, "Don't come -- there is still ten feet of snow, and it is rotting and unstable."
So we got off the freeway at the next exit and spent two weeks circumnavigating Mt. Rainier, a wonderful trip.
Whenever we head into the mountains in Canada, we bring along snowshoes and microspikes, since it is always possible that there is snow and ice at the higher elevations.  If you have never used microspikes, you will love them -- it is like four wheel drive for your boots.