From a 1960 interview that Eddie Shore gave it took him 22 hours. Shore hired a cab driver at North station when he missed the train for the drive north. Between the storm, frozen windows, broken tire chains, driving the cab into a ditch, hiring a horse and sleigh team and finally a getting a train he made it to Montreal around 6pm. He then had a quick nap, and some steaks, played 56 of 60 minutes (with 4 mins of penalty time) and scored the only goal. He was also fined $200 for missing the train.....

Shore describes the windscreen as being an old fashioned split screen so it's likely the cab was an older model. A Model T would have a top speed of 40+ mph rather than the newer Model A's 65mph. So in better conditions, you'd probably be looking at something around 12+ hours to drive up the paved Route 3. There were Road Trails through New England and Canada (for example this 1924 map for New England shows the routes - the numbering was changed in 1927). This 1927 map shows the roads in Quebec

Source Eddie Shore and That Old-Time Hockey - C. Michael Hiam