I used the CX bike when it was snowy, we only had about 6-8″ of snow so not too bad. Schwalbe Snow Stud tyres, back roads, canal towpaths, urban parkland route to avoid all the total muppets in cars.
The snow isn’t the problem, it’s the fact that almost no-one has any clue of how to drive in those conditions.
A couple of years ago I was driving through Yorkshire in the snow and there was a BMW in front of me doing 35mph-ish on the straights then he’d slam the brakes on at every slight bend in the road and inch round it at 5mph then gun it back to 35 again. It was SO frustrating being behind him. Idiot!