Hey I’m new here and trying to be active, and being a chemist, this is a question that is right up my alley. So I will share with you some of what I know!! I will try to be a little technical and give a full explanation as to really try to answer your question, sorry if I ramble….
Peppermint has a high menthol content. Menthol has local anesthetic and counter-irritant qualities, and it is widely used to relieve minor throat/skin irritation and congestion. A counter-irritant is a substance which creates inflammation in one location with the goal of lessening the inflammation in another location.
So basically, without causing a change in actual body temperature menthol can trigger the bodies (TRPM8) cold receptors giving you the perception of feeling cold, much like eating a spicy pepper will do the same but with a hot impression, while at the same time inflaming the treated area.
In short using too much, or too strong of a solution of pure peppermint or eucalyptus oil extract will have a higher percentage of menthol and may temporally “numb” the area. It is used for that purpose in tons of topical analgesic sprays, ointment, and oral medicine to cause temporary relief of minor pain, and in health and beauty products to give a minty fresh feeling to your mouth and skin. However if a smaller less pure form of the oil (like “peppermint extract” you could buy at a candy shop) is applied to the skin especially to a mucous membrane (like your vag) you will get a slight amount of swelling which raises capillaries and makes them much more sensitive, combined with a very cool tingling sensation. So yes, I could see how that would feel good if you rubbed it into your clit or on your nipples. Just like the feeling in your mouth after you use mouth rinse.
But to answer your question by the book…. Currently there are no long term reported adverse nutrient or herb interactions that involve menthol, at least in lab animal testing. (−)-Menthol has low toxicity: Oral (rat) LD50: 3300 mg•kg−1; Skin (rabbit) LD50: 15800 mg•kg−1). Which means it is harmless to rats and rabbits at 50x the safe human dose. As far as animal studies go, that is a very good indicator that humans should have no adverse or long term effects from using menthol in any way.
So until, or if, scientific studies prove otherwise it is safe to assume that even in relatively high dosages over an extended period of time this should have no lasting effects on any part of your body. Just like brushing your teeth three times a day with menthol loaded toothpaste, or sucking on peppermint candies has any long term effects on your taste or mouth sensitivity, with the exception of long term medical grade pure menthol extract being used to treat sensitive teeth. But then again, that only works during the course of the treatment and is not permanent.
There are tones of sex-acts involving mint; such as “the peppermint swirl,” where a woman would go down on a guy immediately after brushing her teeth, or where a guy will go south on a woman with a hard peppermint candy in his mouth. I have had this done to me and have done the latter on several occasions and it is quite pleasurable!! When we were studying the properties of herbs way back in my junior year of school there was a sex-toy that was supposed to incorporate mint oil into it. We kept watch of it out of curiosity but it never got its patent approved. Here is the link to the patent for device if you are interested.
Hopefully this long winded post managed to answer your questions??