Planning a late winter trip to Glacier National Park

Trying to plan a major trip to Glacier National Park during late winter. We'll be driving (pulling the Silver Streak) so access with a trailer when we go will be important. We'd prefer to camp in the park somewhere if possible. The goal is to get some winter/snow action but not going in the dead of winter. So I'm looking for any advice as to when/places, etc... We were thinking about late March to early April. Any advice would be helpful and appreciated.