It was kind of shaped like a squat can of beans, except for the fact that it was mostly clear (you could see the transistors), it was blue-ish in color and it had a light inside of it when powered on. Now I suspect that it was laying around the house year-round, but for whatever reason I only, as a kid, noticed it around Christmas time.
With a bit of researching, I was actually able to find the make and model of the radio. It was a GE Blue Max P2760 Blue Police Light AM Transistor radio.
The purpose of the radio? Why to listen to the broadcast of Santa's progress, as reported by the good folks at NORAD. These days, but the way, NORAD broadcasts this on-line; you can find it HERE.
For whatever reason I remember the house being dimly lit when the radio was being used on Christmas Eve. That was, I suspect, all part of the plan, namely to make four little boys sleepy on Christmas Eve.
On another note, while I don't collect radios, I do have two vintage radios in my office. The first is a terrific Sony table radio that actually works really, really well. The second is an actual Kmart brand radio from the early 60's that I'm quite frankly afraid to even power up. The Blue Max will be joining that small collection, courtesy of a seller on Ebay.