If you can make it work, it's well worth sorting out the tires to ride on ice -- it's a heap of fun. First off, it's a lot easier to lock the back wheel and slide, so even I (with no skills to speak of) can get 20,30,40' slides no problem; secondly, it's a lot easier to get enough power down to slide the back wheel out when accelerating, which isn't good for much but makes me feel like I have studlier legs than I really do..

Thirdly, fixie on ice is the way to go anyway, because you can tell just when things are starting to lose traction at the back and deal with it. A studded tire on the front is a very good idea, and the back'll help, but it's not as necessary.

The main problem I have with riding on ice isn't that my wheels don't grip, it's that when the wheels go it's usually because it's so icy that putting a foot down won't help, because my feet just slide as well. One time I tried to stop at an intersection where a lot of cars had been trying and failing to stop, so it was just a bit 20x20 foot sheet of ice they'd polished up; slowed down gently, just as I was stopping a wheel slid, my foot went down, foot slid, I went over, and it was so icy I ended up literally having to crawl out of the road and pull my bike after me. No fun, and that's when I realised I definitely wanted studs..

Once it's been frozen for long enough, go hit the lakes -- if you can find one with pressure ridges to get air off, so much the better. A less painful alternative but still with the sliding-around fun is fresh snowfall over grass..