I have never had a dérailleur seize, freeze, or otherwise become gunked up on me. Not riding through a foot of snow, not in -20F temps. Like the poster before me, sounds like poor choice in lubricants.
Road or mountain, neither one is going to be more prone to shifting problems. Fenders are a difficult fit on roadies, but then you can go with a cyclocross or touring frame which are designed with more clearance for bigger tires. Whether or not you want drop bars in snow is the question.