I went out there today on my MTB, and you're right. It was hard to stay up. Thankfully, I did switch out the clipless pedals so that I could ride in my boots. 3 miles in 7-8 inches of the stuff and I was ready to go home.
I found that the trick to staying upright was to not make any sudden front wheel adjustments. If I did, I'd start to tip over to the side and then I was doing doughnuts until I fell over.
Keep it as straight as possible so that the rear tire rides in the front tire's tracks, and it's kinda ok. Until you get to wet slush-then you're walking.