I lived up there for ten years, and have done minimal winter trips in the park, mainly because it is a hard place to get into. The peaks are steep, the valleys are deep, The avy danger can be extreme, and you can bet on waist deep snow! the park has to different personalities, the east side of the park tends to be sunny, windy, and cold. The westside, temperatures are more moderate, with calm cloudy days, and DEEP SNOW. Take this with a grain of salt, old man winter will dictate what G.N.P. will be like.
as far as recommendations, Como park, from MCdonalds lake will get you to the backcountry . It.s about six miles in.
Although not in the park, Jewel basin is a popular winter playground,for backcountry skiers,and snowmachiners,, Check out the glacier Mountaineering Societies web site for up to date beta.if your not set on Montana, Colorado is a great place for backcountry winter trips, Sunny days, windy, so the snow tends to pile up on certain sides of the mountain, making the other aspects almost snow free, and travel easy.