For what it's worth, I've winter commuted in pretty harsh conditions over a couple of years' time in the past. I also get snow and ice where I live now and where I've commuted for years.
I've always been successful with just knobby tires on a mountain bike. I've never had better than v-brakes.
I don't doubt that studded tires would provide some extra margin of safety on the iciest days, but I can say that I've gotten by for years without them. A friend of mine has studded tires, but with the road plowing and sanding he says there aren't that many days in the year when he thinks they really make a difference.
When I was living in very cold, snowyville, U.S.A., with winters about as snowy and cold as they get in the lower 48, there was a guy who would ride his road bike out in the winter time. No studs, no knobs, just himself against the road. Even there, the roads were well enough maintained that the guy could get out almost all days he wanted in the winter.
Anyway, I find stopping distances are certainly increased on snowy or icy days. No question. Disk brakes might improve this performance. I go slower, though, anyway. I believe it's possible to ride in reasonable safety with rim brakes.
I'd highly recommend some kind of fenders, too.
There are plenty of good tips in the ice-bike forum, too. Good luck.