Is there horse pee in monster energy drinks?

No.

Like most energy drinks, Monster drinks include taurine, an organic acid which can be found in the lower intestines of many animals, including humans and bulls. It is because this chemical was originally found in ox bile that rumors started about the source of taurine in food products.

Any taurine that you see in an ingredients list will have been synthesized in a lab, not extracted from an animal.