Our bedroom was similar, except the closets were on the 2 interior walls. This effectively insulated the master bedroom away from the rest of the house. It got very cold in there!
We had 2 non insulated exterior walls, then a poorly insulated attic above, and an integral (but freezing and not insulated) garage below.
We went the non-diy route, there was a lot to do. Getting the insulation blown into the attic was relatively inexpensive. Also, we were able to get it blown into the ceiling of the garage (ah, heaven, being able to walk in my bedroom barefoot!) The expensive part was the exterior walls, we had it all blown in from the outside. They drilled through the mortar in the bricks.
Hands down the best home improvement we have done, with the possible exception of replacing the 50 year old aluminum single pane windows.
Oh yeah, we did actually DIY one part of it, the garage door! That cost about $150 in pink foamboard, special nails for the foamboard, and 2 types of flashing. Before this we could actually freeze water in the heated garage some days. Now the garage stays within about 10 degrees of the rest of the house. It looks stupid to have pink foamboard nailed in sections to the back of the garage door, but it's comfortable in there!