Insulation, Radiant and Vapor Barriers - insulating a raised ceiling

My family room has hardly any insulation, it looks like they removed the ceiling exposing the rafters in the roof. I like the look of the exposed beams but somthing has to be done to insulate this room better. A day after a snow fall the roof over the family room has no snow left on it while there is still plenty of snow over the rest of the house. Right now it looks like the only type of insulation is what looks like sound proofing tile in between the rafters. Is there a good type of insulation I can put over the tiles and leave the beams exposed or would it be best if I stuff insulation up there and sheet rock over everything.

Thanks, Kevin

Rigid foam insulation, as used in cathedral ceilings, may be an option.

http://www.resercon.com/Insulation.html