Actually it is "paws" according the all the lyric sites.
That's (from Merriam-Webster):
paw
verb
pawed; pawing; paws
Definition of paw (Entry 2 of 2)
transitive verb
1: to touch or strike at with a paw
2: to feel or touch clumsily, rudely, or sexually
3: to scrape or beat with or as if with a hoof
4: to flail at or grab for wildly
intransitive verb
1: to beat or scrape something with or as if with a hoof
2: to touch or strike with a paw
3: to feel or touch someone or something clumsily, rudely, or sexually
4: to flail or grab wildly
5: to search especially carelessly or roughly pawed through the box of discount items
I know I’m splitting hairs here but, all of the lyrics I can find use pause. As in the reindeer pause their flight so Santa can leave the presents. Also, if it was paw as per the definition used it would be reindeer paw not paws.