Something (or someone) that's soft, snuggly, and huggable is cuddly. Your pet rabbit is so cuddly that you wish you could bring her to school, so you'd be able to hold and hug her all day long.
Some people are naturally cuddly, either because they love to hug you, or because they're particularly plump and comfortable. The same is true for animals and dolls — there are some things that seem to be made for cuddling. Cuddly comes from the adorable word cuddle, which probably stems from the obsolete verb cull, "to embrace," or possibly the Middle English couth, "known" or "comfortable with."