Originally Posted by
bpeder
...But short of having legs like a Percheron horse in the prime of life, I don't see how you are going to power through snow that deep. ...
+1
Even if skinny tires can cut through it, I'd be exhausted in short order. With snow that deep you're not just pushing your tires through, but your pedals as well. Plus you're dragging your chain and your derailleur (if so equipped) through it.
There's people in Hawaii that ride with surf boards attached to their bikes. There must be a way to carry skis, poles and a set of snow shoes. Ride as far as you can and then strap the skis on.