Santa Claus appears and is referenced several times in Calvin and Hobbes.
He is usually mentioned when Calvin debates how good he should be at Christmas time. He does, however, appear entirely a few times: Calvin once imagined an alter-ego Evil Santa giving destructive presents to bad children and clothes to the well-behaved, leading to Santa's first full-body appearance in the strip (as well as a poem) where Calvin fantasizes that Santa saying "good little kids make him sick" and Bad kids are the ones who get toys. Also, Calvin pictured Santa ranking Calvin's deservedness of presents based on evidence and accounts and worrying about what Santa considered of him. Finally, in a weekday strip, after Calvin snowballs Susie, he pictures the face of an angered Saint Nick frowning down at him.
Santa's most prominent role in the series was in a Sunday strip in which he discusses Calvin's behavior with one of his elves and decides on a positive verdict, only to observe through a surveillance monitor that Calvin's restlessness is keeping him awake at night. Whether or not this was all imaginary is left ambiguous.
Here are some verses from the poem that Calvin fantasizes he receives from Santa Claus
So now, I urge you: Be vulgar and crude! I like it when children are boorish and rude!
Burp at the table! Gargle your peas! Never say 'Thank you,' 'You're welcome,' or 'Please.'