I've done all of the above.

Just putting studs on the one bike is the cheapest way to go. Depending on your riding style, it can be a pain to push the studs on a warm, sunny, midwinter day.

The second wheelset method wasn't all it's cracked up to be. You still get greasy from the chain when swapping the rear, and it means carry two different sizes of tubes. Yes, it's quicker and easier than swapping tires, but not by that awful much.

Having a second bike with studs on is the easiest and most convenient. I don't have a dedicated winter bike, but instead, one of my two "commuter" bikes can fit the studs.

In the three-seasons, it's nice having that second bike too. Variety is the spice, and when you wake up to find that inevitable overnight slow leak you didn't know you had, you can just grab the other bike.

Besides, N+1 must be obeyed.