It can work in a pinch, but it isn't ideal. Many's the time I've chased rabbits wearing normal, winter gloves, or forgotten my shooting glove and just grabbed a leather work glove out of the truck's tool box. Accuracy might suffer somewhat because you don't get the same string feel, and depending on what your gloves are made of, you might not get a smooth release: a lot of gloves have grippy, high-friction material on the fingertips, which will tend to grip your string instead of letting it slide off. It can wreck your winter gloves, too, since many of them aren't really built to withstand the pressure of string release.
For serious cold weather hunting, I wear a shooting glove under a thick pair of convertible mittens, the kind Tajue mentioned, with the hand flap that folds over the fingers. That way I can keep my fingers warm until I need them. Once you flop the top off, it's business as usual.
