You shouldn't have any problems with snow, but no guarantees. The weather is very unpredictable in the mountains of Montana. The Meadowlake golf and ski resort is a nice place to stay (Whitefish, MT) and is a short drive to the west entrance to the park. Can't help much with the rest of the trip as I usually stay in motels. Glacier to Waterton and then up to Banff is truly one of the most spectacular trips you can take. The Canadian rockies are rugged and beautiful. A stopover in Calgary can also be a lot of fun as they have a zoo, olympic village and lots of beautiful sites. Don't miss out on lake louise and lake emerald when in Banff, nothing quite like them.
Bob