If you have enough clearance, I would install Nokian Hakkapeliitta 700x37 tires on your hybrid, as well full fenders and a long mudflap. Otherwise, use your junk bike or get another "new" junk bike.
By the way, in Montréal, I find that knobbies are almost essential, but that studs are "gravy". I had tried an Innova studded tire a few years ago and quickly replaced it with a non-studded knobby which provided me more comfort and more traction. Then I broke the bank and bought a set of Nokian Hakkapellittas, which I use about 2-3 weeks per Winter at most. But then, I ride on the busy throughfares of MOntréal, the Plateau, Rosemont and Outremont, not on less used streets.
What do YOU think you'd like to do? :-)
If the bike is your fit but you're still unhappy with the 'bike' then may be save the money on new parts and exchange the bike. Whatever pleases you and gives you satisfaction/pleasure within the 'budget'.
By the way, I couldn't do what you guys do in winter in your area . . . Some serious weather!