My DS is nearly 3. He likes to be cuddled and will come onto our laps for a snuggle, but he has never put his arms round us and cuddled.
When I show him how to do it, he screws his face up and holds it away as I cuddle him and put his arms round me.
My DD is nearly 15 months cuddles "properly" all the time.
Is it normal for a 3 year old not to cuddle?