OK, a psycho/social/cultural analysis of this favorite Christmas song (or close to it...my comments in bold italics.)

I saw Mommy kissing Santa Claus
Underneath the mistletoe last night

Voyeurism, most definitely...BTW, how many people have actually caught their parents in an act of infidelity and wrote a song about it? One, obviously...the rest are country songs where Santa Claus is also their uncle and dad. Let's move on, shall we?

She didn't see me creep
down the stairs to have a peep;
She thought that I was tucked up in my bedroom fast asleep

Clearly, a need to create the illusion that one is well-behaved and doing what one is told is important to the protagonist of this story. Some kind of neurosis or obsessive/compulsive disorder?

Then I saw Mommy tickle Santa Claus
Underneath his beard so snowy white;

Electra complex, as defined by Freud, is when one is romantically in love with their father. Is there something the songwriter isn't telling us? Also, the choice of a heavy-set, older man as opposed to a younger, thinner one (aka "Daddy", who we never hear of except in passing) is also interesting. Just a sexual preference, or is "Mommy" equating physical size with success?

Oh what a laugh it would have been
If Daddy had only seen
Mommy kissing Santa Claus last night

Obviously some discord between the "child" protagonist and Daddy, and/or a sadistic streak. Why else would a child want to see their father go through emotional angst? Borderline personality disorder, or is it possible that the child holds a deep-seated resentment towards the father for (if male) not buying him a BB Gun or (if female) missing their debut as the Sugar Plum Fairy in the 3rd grade production of "The Nutcracker"? Perhaps the child is just a self-satisfied, spoiled, materialistic BRAT.

Well, gee, I like Christmas just as much as the next person, but these things just run through my head and I have to share them!

In Christmas Love and Analysis,
Sudiegirl