In a standard deck of 52 playing cards, the only king card not to have a mustache is the king of hearts. This is because a lot of people tend to associate the heart with being the most pure organ in the body. Due to that, the heart doesn’t wear disguises, which a mustache can be used as.
So, the king of hearts is clean-shaven.
However, there were rumors that the king of hearts is supposed to represent Charlemagne, whom is often depicted with a beard and mustache, so there may be no truth to this or it may have morphed.
That said, there are decks that depict all four kings with a mustache. So, overall, it really depends on who made the deck you’re playing with.