They are designed to help the horse breath easier should the horse need help. They are called Equine Nasal Strips. Same principal as on human athletes and partners that snore. LOL! (They are not allowed in racing.)
I googled them "H&H equine nasal strips" and there's a very good article about them.
Nope no need to soak them off. They peel off very easily with no/little sign of discomfort or any hair being pulled from the skin. They're generally used at the higher levels of eventing (CIC * and up usually)