I think in general there is more than the usual amount of snow on most of the aproaches but not so much as to warrent BIG boots or snowshoes .
The approaches into Glacier Gorge, Spearhead, the Petit, Hallett's etc all have large patches of snow but generally light weight boots or sturdy running shoes suffice for approaches. It's wet coming out in the afternoons but the early approaches are dry just "slippery".