I would say 'cuddle up with' or just 'cuddle', although 'cuddle with' is OK. I wouldn't use 'together' except with 'lets' - e.g. Let's cuddle up together in that rug. You need an article before 'rug' too. So - the last one is the one that I would use, 1 is ok, 2 is not, and 3 needs a little work...