This month's joke is based on the expression long face.
As you know, a horse, compared to a human, has a long face! We can use long face to describe someone's physical appearance e.g. "I have a long face but my brother's is quite round."
As an idiom long face means to look unhappy or sad:
"Why has Simon got such a long face?" "He failed his exam."
"She's got a long face today because she just broke up with her boyfriend."