December is completely fine and one might encounter snow in Mussoorie and Nainital and it looks magical.
December in Mussoorie might cost you a bit more because of the Winter line festival, which is quite popular and huge crowd would be there.
Shivanand Hulyalkar, of-course December is best month to Visit Nainital also, it's an tourist peak time to visit. You can also see snow fall in Nainital in December so it's hardly advisable to pack your all winter staff & gears along with you. Well 7 days are good enough to visit both places and you can really enjoy your holiday, there are so many beautiful place you can visit in Nainital & Mussoorie.