First thing to do is decide what kind of handlebar you're most comfortable on. Flat bar like those on a mountain bike and I'd say a hybrid which are often supplied with mudguards and occasionally a rack ready fitted.
Drop bars like those on a road bike and your best bet is a touring bike which are almost always supplied with mudguards and a rack.
Both types generally will accept bigger tyres with snow studs and a nobbly tread. For those, you'll want bigger (50mm+) mudguards.
Both will generally weigh a fair bit unless you're spending serious money.