Last winter I posted up this picture of the cover to my breaker box.
basically you had outside siding with holes that wires ran through but no caulking then a loose fitting 3/4" plywood board on hinges and then inside. The drafts and cold from that corner of the house were very obvious. I couldn't think of a good fix until my wife said just build a box and seal it properly like an outside door.
So I caulked the holes closed. Added as much insulation as I could to try and keep the cold in that one area then built a frame and door for the opening.
the door is 1"x2" frame with 3/8" skin and 1/2" foam inside of it. The box is 1x4 and a lip of 1x2 I caulked the seams on the box and added some foam tape.
I use a small barrel bolt to keep it closed up tight.
I caulked the box to the wall and all that is needed now is some paint. It's not as nice as what a cabinet maker would produce, but it's a hell of a lot better then what I had.
All of the wood and foam was scrap from other projects. Foam tape was $10 and the hinges/bolt were $3 each so the total cost of this was under $20. It took me 3 or 4 hours spread out over 2 weeks since I worked on it while both kids were awake but would leave me alone for 5 minutes.
The room is noticably quieter with most traffic noise that used to be audible now being gone. We'll see if it makes much of a difference this winter.