I don't ride in the snow. But we get a lot of rain around here.
I've used a single bike for commuting for years.
I've finally dedicated one bike to winter commuting which means it gets much of the water/road grime/etc, and am experimenting with "commuter tires" on it.
How frequently do you desire changing from studs to studless? I'd find changing tires on a regular basis to be a bit of a pain, so I'd either go with a spare set of wheels for a quick change, or a spare bike.
I'm also a roadbike commuter, but I think most of the studded tires are MTB sizes (and probably appropriate). So, that might also drive one's bicycle choices.