I would go for an 80's mtb ie no suspension
I'd echo this or a 700c hybrid. It'll last two years; your wheels will probably give out first. Cantilever or disc brakes (not hydraulic due to their freezing point).
In terms of tyres Schwalbe Ice Spiker Pro or Continental Nordic Spike - both have 240 spike options. Be aware that these'll be slower and heaving, but give you lots of traction. There's less 'spike' options available which provide a smoother ride but less traction in ice.
Alternatively, have a read of this; The Cyclist Who Went Out in the Cold by Tim Moore - he rode through Finland over compacted snow and ice on a 20" wheeled shopping bike. Or maybe not as his comments about riding over ice aren't publishable on here. Basically he went N to S when S to N would have been more sensible.