Gravel bikes have drop handlebars, narrower tires (35-50mm vs. 2.0-2.6 inches on a mountain bike), and no suspension. They ride well on gravel and dirt roads, but they are not designed for trails with rocks and roots. Mountain bikes are built for that.
For most recreational cyclists, yes. You'll lose 2 to 3 km/h on average on pure asphalt, but you gain access to many more routes. If you race on the road, keep your road bike and add a gravel bike as a second bike.
Between $1,800 and $3,500 for a reliable gravel bike that will last. Below $1,500, compromises are made on the brakes, groupset, and wheels. These are the most expensive parts to replace later, so it's better to get them right from the start.
With studded tires like the 40mm Schwalbe Marathon Winter Plus ($119.99), a gravel bike can handle packed snow and winter gravel. For truly deep snow, a fatbike is still necessary. The gravel bike mainly extends the season by a month in spring and a month in autumn.
40 mm is the sweet spot for most Quebec terrain. More gravel or forest paths: go up to 45 mm. More pavement than gravel: 38 mm will do the trick. Below 35 mm, you're essentially riding a road bike.
Expect to pay an extra $50 to $100 per season: brake pads wear out faster due to abrasive dust, and the chain gets dirty more quickly. Nothing dramatic. However, frequently cleaning the chain can double its lifespan, so it's worth doing.