As I understand it, the EASA Mountain Rating is only available at, and required for, some Alpine airfields.
No rating is required elsewhere in EASAland, nor in the US or Canada.
Some Flying Schools in US and UK offer mountain flying courses.
Colorado Flight Centre required a renting pilot to have completed their course before landing a rented aircraft above 7000'
I've never done a mountain flying course, although I enjoy flying in mountains.
The highest airfield I've used (solo) is Gunnison, Colorado, 7600'+.
If you want to fly in the mountains, in your own plane, I'd suggest glider ridge soaring as training.
If you rent, you have to do what the FBO requires.
If you just want a signature in your logbook, if there's a cheap course in East Anglia or the Netherlands take it.
Weather is important, and there are big differences between high, hot, dry and not-so-high, cool, and wet.