There are 2 reasons for aging the characters. The primary concern is the taboo of underage sex. The second is that they can get older, more skilled actors to play the parts, as is the case with Bran, Rickon, Thomen, etc.
Also, a lot of time is supposed to have elapsed in the books by the time it ends. It's a unique scenario given that the seasons last for unpredictable periods. So by the time "winter comes", the Stark kids will be young adults with adult problems, so having older actors will make it more believable down the road.