I doubt if there's any real significance. It's just that if you have a big house with numerous rooms, you have to distinguish between them; and for those rooms without a particular function (eg library, dining room, master bedroom, ballroom etc) the colour of the walls was (and is) the easiest way. There are possibly as many Red and Green Rooms in big houses as there are Blue.
No but there aren't. The other rooms like you say are named after functions, but this is the only room that is named after a colour, its also very common.
It was probably a fashion. If Prince George liked blue and had a Blue Room in his palace, then Lord Shrewsbury or Lady Snetterton or Sir Nigel Snootstonby or whoever would have a Blue Room in their country mansion, just to imitate royalty and show their 'taste'. Then before long everybody with a country estate would have a Blue Room in their house.