My winter bike has studded front tyre, while the rear one is with just small knobs (Continental Race King). The front tyre is Schwalbe Marathon Winter. It rolls very fast even with studs. If inflated to a higher pressure, studs almost make no contact with the ground.

So my solution is simple - ride the winter bike with tyres inflated to a higher pressure. In case of more snow/ice, I just stop for a minute and deflate tyres a bit.

But I rarely risk riding the "summer" bike if there's even a slight chance of snow.