vermontanaRight now conditions are not too ideal for touring away from resort sidecountry, but we are starting to get some snow now which will help approaches fill in. With this though, avalanche danger is starting to increase so please have proper training and gear and check the Flathead avalanche forecast before heading out.
Rocky Mtn Outfitter in Kalispell is a great resource to check out if you can, they sell a guide book there and the shop guys are super willing to help you with route recommendations and current conditions. Great Northern Cycle and Ski in WF might also have a guide book and local knowledge.
Glacier: tends to have super long approaches in winter but there a couple options that have some info online. Mount Brown lookout (6ish miles, 4200 vert, brutal approach) Apgar Lookout (5 miles 2000 vert, easier approach). Starting in town of Essex (southern border of park) there is a lot of good stuff in Great Bear Wilderness, look up Lake Marion tour. Marias Pass which is east side of the park has some good tours, but is a bit far from the Flathead, there should be some good info online for that area.
Flathead: Jewel Basin/Camp Misery is probably the best backcountry close to the valley, depending on how far up the access road you can drive though it can be a very long approach, best to have a snowmobile. Should be some online info for that. The Swan Range farther south has a lot of cool stuff too but I've never been.
Whitefish: best stuff is sidecountry northeast off of the resort into Canyon Creek drainage or other drainages southeast of the resort boundary, otherwise a snowmobile is pretty necessary for approaches to other lines in the Whitefish range. you can skin up the uphill routes at the resort to access.
Hope this helps! feel free to PM me.
These are all some super great options. Camp Misery and Canyon Creek are dope spots. The Swan Range has some good terrain, but I definitely would not go without someone who knows the area. Mount Stimson also has legendary terrain at the foothills, but super sketchy bushwhack and approach.
Whitefish's sidecountry is pretty good. To the west of the resort, there is a "peak" called Ghoulies with pretty good terrain and an easy approach.
OP: feel free to PM me as well.