the difference is, asking to do an act of hugging or asking to give a gift in the form of a hug, like that is the expression

I would say that there is no difference in connotation/meaning (they mean the same thing), they are more or less interchangeable. Using one over the other seems more stylistic than anything else. 

I agree with Oz. Its better if you say, "Give me a cuddle." or "Can I have a cuddle please?"

If you ask that to someone you might look a bit odd. Its better if you say give me a cuddle or "can i have a cuddle please" is a cute way to ask :)