I like your style, Paul. Mountain biking in the snow! Maybe you could figure out a way to lock the front wheel, add a skid to it, and sort of snowplow around the New York countryside.
Actually, you can make your own studded snow tires. To do so, buy some boxes of quarter- and half-inch sheet metal screws, preferably with round pan heads. Then, get some old knobby tires and drill small holes through the knobs, along the sides of the front and rear tires, and also down the middle of the back tire. Next, dab the quarter-inch screws in some epoxy and screw them through the inside of the tires. Do the same for the half-inch screws around the center section of the rear tire. Wrap some duct tape over the exposed screw heads. After the whole thing dries, clip the stem off an old tube, split it down the middle, and affix it to the inside of the tire with contact cement or more epoxy (you want to protect your working inner tube from the metal screw heads, of course). Hey presto, homemade snow tires.
Alternatively (for readers not prone to MacGyver-esque fixes), here’s one prepared earlier: the Schwalbe Snow Studded Tire. I haven’t found any retailers in the U.S., but the Mountain Equipment Co-op in Canada sells them for $56 Canadian, or about $35 U.S. Or, most any mountain bike tire with deep, widely spaced lugs will work moderately well; closely packed lugs will tend to hold the snow. And of course, such a tire will work pretty well in spring mud, too.
The Mountain Equipment Co-op can be found online at: .