Is it OK to use regular conditioner on a one year old's hair?

Our 1 year old son has dry hair, which is worse in the cold dry winter air. (He also has eczema which is a related condition.) It is particularly noticeable on the back of his head. It feels like straw! We have Aveeno moisturizing shampoo, but it only helps for a very small increment of time. I was wondering if we could put a tiny bit of regular/adult conditioner in his hair. Would that hurt him? Or is there anything else I can do to help this condition?