I'd stay clear of the bike in icy conditions, however, if I was forced to go out, I'd choose my old MTB conversion.
26x2.0" Marathons (probably deflated a little), wide, flat bars and no SPDs
It's slow but it feels really secure and I could bail-out more easily than on my road bikes with SPDs, drop bars and high top tubes.
If it got really silly then the MTB would come out but it's still bloody scary on downhill corners on tarmac and compacted snow.