The gasoline in your vehicle is subject to the same cold weather (but not quite as hot as a summer garage).
But if you do not need the gasoline always readily available, put it into your gas tank and then only fill the gas can when you need gasoline (like summer, for mowing lawns) and it will be fresh gasoline.
Not if the garage is attached to your house. A locked back yard shed is a better choice if it is.
NO! If you store it in a sealed container with the freezing weather the can will be destroyed and then the gas leaks. If you must store it leave an air vent open so the can does not collapse but this risks fumes in a closed area. Better choice is to use it before the cold weather sets in.
Store it safely. If the can is not full, you need to add a stabilizer so it doesn't absorb water into it as it condenses in the can. It won't get cold enough where you live to freeze gasoline, or hot enough for it to burst into flame.
Do not store gasoline longer than 30 days if you can help it, 90 days if untreated, 180 if treated.
Wouldn't do it , flash point of gasoline is too low. With a minor leak the place could go up in a bang with just a static spark . You need to keep it in some place well ventilated same goes for propane tanks. Two gallons will take you and a ton and a half of vehicle 40 miles, imagine what it can do to your house.
The amount you may LEGALLY store in your garage is governed by local fire prevention code. In some places it's 2 gallons, other than what's inside tanks of machines. In other places it may be as much as 10 gallons (e.g., NFPA 1(2009) 66.9.6.2.1.
Yes, you can, but you shouldn't. A gas can has a really primitive vent, and is a fire hazard stored inside of a garage; cars have a basically sealed fuel system, not at all the same. Ask your fire department.
Then there's preparing the fuel for storage, to "stabilize" it from chemical breakdown, using - a gasoline stabilizer, like "Sta-bile". Use this "religiously". Don't worry about the gas freezing, as that's like around 40-50 below zero F, and your machines wouldn't run anyway, you would have left the area, or would have died.
Best set-up, to me, is a shed apart from the house/garage, for both the machines (mower, snow-blower, chain saw, gas line trimmer, gas cans - and any spare LPG tank for the grill, etc.). For just a can of (stabilized) gas, I'd more likely put it completely outside, like at the side of the garage.