Just a thought, but Q-Dave keeps the road to Lac La Croix village open all year long. Why couldn't you park your vehicle at start of road into Beaverhouse and IF you had a snowmobile/sled, you could go into Beaverhouse, and walk into lake or walk/ski down into Quetico? Or jump into Cirrus.
IF you had a good 4x4 and parked close to gravel plowed road, you should be okay I would think? I don't think it's agaisnt the law to drive a snowmobile into the parks borders and stop, or is it?