Eswense, I'm not an energy engineer, but I have dealt with sound and energy issues with door and window insulation for over 25 years. Here's what I have to say about your situation: your bedroom sits next to an unheated part of your structure. What you want to do is keep the heat in the heated part and not worry about the garage.
Looking at your pic, I see what appears to be a garage with no insulation in the walls. I'll bet that goes for the ceiling too. Once energy escapes to that garage, it will not be retained by adding insulation to your metal door. It has too many places to be lost through convection or conduction. There will be a small amount of radiant loss as well, but that gets complicated.
I think your best bet would be to add insulation between the unheated portion and the heated portion even if you have to add a stud wall outside the bedroom in the garage. Make sure your existing wall has insulation in good condition inside. There are ways to retro install insulation in that wall.
Also, if there is a passage door to the garage, make sure it is weatherstripped. It goes w/o saying energy efficient windows help. Lastly, many studies show the majority of heat loss at the ceiling. How is the existing insulation above your bedroom?
If you decide to heat the garage to keep it above freezing, do a total insulation job in that space. And yes, there will be slightly less energy loss through to the garage for each 10 degrees you bring it closer to the house temps.
Insulation slows down the transfer of heat. It doesn't totally stop it.
