My opinion is that felines and cuteness make this very distinct from the other question. >_>
Anyway I'd put it like this:
They both climbed into the bed, snuggled up like kittens and took a catnap together.
Or if you really have your heart set on cats, perhaps just a nap because using cat twice just sounds bit redundant. The only problem is that a nap is generally supposed to be considered short but as a lifelong cat owner myself, well, let's just say they get plentiful amounts of sleep plentifully long enough...