Absolutely! When I lived in NJ (moved south in 1986) I owned a '32 Ford Victoria (Vicky), and a 69 GTX. Drove them both on a regular basis through the majority of the Winter. clear sunny (but cold) days are in no short supply during winter months. the roads are not snow covered for the entire Fall, or Winter, or early Spring, so there is plenty of opportunity to enjoy your classics. Rainy or snowy weekends or snow covered weekend are the opportune time to take care of maintenance, mods, repairs, etc.
Owning a classic in the North is definitely viable.