If you go up the winding way from the snowshoe inn you'll be fine. The roads are maintained and traveled regularly so its no big. You can also try to go up the backside with any kind of vehicle at about 5 mph. I recommend taking the main route, also you're going to want to grab some delicious food from the shop at the bottom anyway. Enjoy your trip.
I have no issues getting up in my FWD Hatchback there's is times where it's been slow in heavy snowfall or ice rain where I've struggled but I've always managed to make it up.
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