Slicks, unless there is snow or melting snow and ice on the road (which does happen a few times a year here in Atlanta). The closest we've come to "ice-cycling" was our local tandem club's "Christmas Lights Ride" two years back. We had snow several days before the event and several days of 30 degree temps. We headed out for our ride with the temps hovering in the low 30's and, while the roads were mostly clear, there were still a few patches of hard-packed snow/ice in shady areas that we crossed oh so carefully. Anything less than studded snow tires would have had negligible effect if I had attempted a turn or applied the brakes while crossing the white stuff.
For those times in the past when I've ridden on snow-covered roads (pre-tandem in Calif, Wash DC, IL, PA), I've ridden my off-road bikes with knobbies or Nokian studded knobbies and left the road bikes hanging in the garage. I would do the same for the tandem, e.g., opt to use our off-road tandem with it's knobbies or, if it was something we were doing a lot of, fit Nokian studded knobbies. If we lived somewhere above the Mason-Dixon line where riding in the winter meant riding on snow-packed roads we'd probably add a rigid 26" enduro to our stable that would be fitted with Nokians.