Yes, they are both correct. You can say "It is a little cold," "It is a bit cold," or even "It is a little bit cold." All three ways are common. If you look in the dictionary, "bit" means a small piece, part, or quantity of something, and "little" means small in size, amount, or degree. So "bit" describes more of a part of another noun, whereas "little" is more of a general term. Confusing since they have very similar definitions...

Oh, yes, thanks a lot !