Here's the answer:
* Water: Peppermint will dissolve slightly in water, but it's not very soluble. The flavor you get in peppermint tea comes from a small amount dissolving.
* Alcohol (like vodka or ethanol): Peppermint is more soluble in alcohol. This is why peppermint extracts are often made with alcohol as a solvent.
Important Note: Peppermint is a plant material, and it contains both soluble and insoluble components. So, while some parts will dissolve, others may not. This is why you might see some solid pieces of peppermint remaining in the liquid after it's been dissolved.