I cycled into Cambridge to do shopping today. I rode on Nokian W106 studded snow/ice tyres with a Burley Nomad trailer in tow, on my Dawes Galaxy. I deliberately chose a largely snow/ice covered route (minor roads and cycle paths) in order to test it out. Apart from ruts caused by previous bike traffic, I had no real trouble. Where someone had dug a diagonal channel in the road and I hit it and everything went a bit sideways for a moment, once I'd crossed it, it all sorted itself out and I continued, no problem.
On the way back, I took the cycle path alongside the river. Again, ruts were the issue. One section had had very little traffic, and I wasn't even sure I was on the path at all, but it was fine. Whilst riding on sheet ice on the road I almost lost it due to being distracted by a loose dog, but as the wheel moved to the left and my weight went right, the studs dug in, and I found myself just a bit further out into the road and cycling along normally.
However I finally had to admit defeat in deeper snow on Airport Way. I think I might have had a chance without the trailer, but the combination of uneven surface due to foot prints and the rolling resistance etc were too much, so I got back onto the (entirely clear) road. It was all pretty slow, but it would have been impossible on normal tyres.