The doors are on that side because of where our driveway is, and the building is facing the way it is so that it won't block the view from my wife's office window. I never thought about snow from the roof, my last place had the garage door facing the same way as the roof slope and I don't remember it being too bad. (but, it's also pretty rare that I open a garage door in the winter so maybe I will regret this if I ever want to use it for parking when there's snow)
Not sure about the overhang, this was the size that this truss manufacturer normally does (12" I think).