Back when I lived in Indiana I had studded tires (either Schwalbe or Nokian, probably the former) on our mixte tandem when it snowed. I didn't put them on it because it was a tandem, I put them on because it was the only bike I had with enough clearance. Most rides were just me though, no stoker. No aggressive riding, just a bunch of short commuting runs. While IMO I had better traction than the cars, I still stayed away from all but the emptiest roads. IME car drivers aren't stunning at avoiding curbs and telephone poles in the snow, so I don't trust them to be good at avoiding cyclists.
Treat it a bit gentler than riding on a rainy day with slicks.