It can snow year-round, but any freak storms are unlikely to last. Your electric liner is more than likely adequate for the weather you'll encounter. That said, if you are riding or camping at a significant altitude, expect the morning to be frosty. In camp is generally where I'm looking for the additional layer.
For those planning a visit to Glacier National Park, be aware that a reservation system is now in place for Going to the Sun highway. Planning ahead is required and we can all expect reservations to fill quickly for the weekends.
Enjoy the great roads and consider the roads less traveled. Be aware gas stations can be hard to find on the back roads. That dot on the map has a population under 50 and is the county seat (I jest about county seat but not the population) in parts of Montana.
For more info on Going to the Sun Road restrictions, visit the National Park Service website.