Sure, you can try riding a fat bike on thick snow to get your cold weather bicycling fix. For all intents and purposes, though, we have a feeling using a BikeBoard with your bike is going to make for a lot less hard work on your part.
A ski that attaches to your bike's front tire, it lets the front of your bike glide through the snow. Since the skis out front help compact the snow, there's also less resistance for the rear tire to pass over the same path, making your trek over powdered terrain a heck of a lot more convenient.
The Bikeboard consists of a single ski with a toe and heel design that gradually narrows towards the heel to allow for swifter turns while riding on snow. It comes with a full set of accessories to firmly mount it under the bicycle tire, including a jaw pin, a mounting bracket, boot straps and brake straps. They offer three sizes of jaw pins: one for BMX-sized tires, another for medium-sized fat tires, and a third for really chunky fat tires. Installation is quick -- simply push the tire into the boot and you're done.
Do note, your front brakes are, basically, rendered useless with one of these things strapped in, so you'll have to rely on the rear to bring you to a halt. What if you strapped Backboards both front and back while freeskiing on a steep slope? Well, just remember to jump if you're about to crash into a tree or something.
Available in three colors (green, black, green and black), pricing for the BikeBoard starts at $375.