I live in the middle of nowhere, 2 hours from Montreal. I feel I'm qualified to answer this! :)
I drive a Honda Fit (2011). It goes absolutely fine, although it's quite light, so when the roads aren't cleared (aka: covered in 3 inches of slow) it can drift a bit, so drive carefully. Good winter tires go a LONG way to helping that, though - they're legally required, but it's worth getting the good ones over the cheap ones, and the best tire prices I've found have been at Costco (as in: cheaper enough to offset the membership cost and still save money).
My neighbors drive, respectively: a honda civic and a toyota yaris, and a 10-year-old suzuki hatchback and a Ford Explorer (which we occasionally borrow in the spring, because a Fit gets bogged down on the dirt roads if we're going to the library). Barring the mud-roads in April, though, no one has gone off the road in these smaller cars in the past 10 years, and the ONLY accident any of these cars have been in is because the Explorer hit a deer.
TL;DR: you don't need a big car, you need good tires.