I keep my boat in the garage. This is the first year inside, last year it was outside. I did keep a small tarp over it. I use an ethanol treatment every tank and haven't had issue one. it couldn't hurt to bring the motor into the garage, if possible.
I think if you just run the motor out of gas you are fine. If my boat sits for more than a week or so i run the gas out first. My motor is in the garage but it doesn't get much warmer in the garage than outside. But i wouldn.t like my motor to get rained or snowed on but im sure it doesn't hurt much.
When the temps get down to the 20's I tent my motor with a small heater under it at the lowest setting.
Common problem is the impeller freezing in the housing and tearing to bits when you start the motor. No waterpump = cooked motor.
You can also possibly get water trapped in the cooling jacket which expands when it freezes and busts things up.
Low temps don't effect gas much. Moisture is a year round worry.Use a good additive.