The biggest real problem, potentially, is the extra ventilation. But face it, tents are hardly insulated devices anyway, so it's not as if there will be a huge difference, temperature-wise, between a tent with a bunch of mesh and a tent with not so much. Some, difference, true, but in most cases acceptable. In any event, you can make a three-season tent more winter-friendly by digging it down into the snow, to cut the wind, and to bury the lower edge of the rain fly in snow, so that the fly itself provides a good, wind-proof shell for the tent. Without a shred of empirical evidence to back it up, I've also long felt that laying a "space blanket" on the floor of the tent, reflective (silver) side up, helps keep the tent a little warmer.
Alternatively, you can take the tent as a backup shelter and practice your igloo building or snow cave digging. Either makes a far better winter shelter than any tent aroundwarmer, quieter, and wind-proof. Plus the process of making one helps pass the time while generally proving highly entertaining.
Filed To: Snow Sports