In the last couple of years, we've had a few decent snowfalls where we live (near the Epsom Downs and Box Hill), so we've been able to experiment. My conclusions:
Fixed wheel - sounded good in theory, but was a nightmare. It's impossible to maintain the correct cadence on a frictionless surface. Every time I hit ice and I turned the pedal too fast or too slow (i.e. all the time), I came off. And (as somebody else said) you can't dab a foot down for balance.
Best road bike - OK on ice as long as you are intending to go in a straight line. If you hit ice on a bend, you'll come off when trying to corner. Not bad in snow, apart from the tendency of spray to freeze onto the brake calipers (mudguards? What are they?
) meaning that the brakes don't work. I only found this out when descending the long steep straight road I'd chosen in preference to the less-steep bendy road to avoid the ice-on-corners issue. Plus, the heartbreak and paranoia of checking for damage after each off is not fun with a "best" bike.
MTB - generally my preferred option. My tyres are pretty grippy on packed snow, disc brakes still work, and I'm quite experienced in falling off the bloody thing.
Windcheetah (Tim's) - impossible to fall off, and he was insufferably smug about this fact until he took it rattling down a road that was sheet ice, and spun off sideways into a ditch smashing a hub in the process.
It was a long walk home.
Streetmachine (Tim's two-wheeled 'bent) - gets a bit expensive if you fall off and bend the under-seat handlebars, which is all too easy to do.
Tandem - absolutely insane idea, but it seemed to work. Extra weight on the tyres cut through the snow to solid ground, and we have a drag brake on there which can be used when the rim brakes are iced up.