Many are easy to spot if you know what to look for.

If you do a lot of terraforming, then you should be familiar with how steep a slope can get.

When the game creates the mountain cave on a mountain side, the game creates an almost vertical slope on the mountain that is unobtainable from terraforming. So I just run around looking for these vertical slopes and there is always something there, usually a cave, but sometimes it can be other things like an egg.

Tx for the replies. Guess I'll keep looking

Not common enough IMO.

I swear. I went back into the game, and found one not 50 meters from where I dropped my last portal, just on the other side of a big rock.

put the seed of your world into this, if you wanna see.

https://valheim-map.world/

or random seeds, to get a sense without a spoiler.

I've found 12 without venturing too far at all. It's like everything else in this game, RNG (PNG?) is either with you or against you.

I did a couple of random maps for you and see about 100 total, give or take. None in the far south hot lands even when snow capped, but a few in the far north. Large ranges had as many as 10 a few times; typical mountains have about 3-5, and any number of small blip mounts have 0.

They can be hard to see. The mountain likes to blizzard and fog up, and the entry is the same grey rock color you see everywhere. Its obvious when you spot it, usually from relatively close, but I would not count on it from far off.

Big/very big mountains have 5-6 caves
Little peaks only have 1 with luck
I was looking for new seeds while ago ( 1 hour in the generator ) and its was i watched

I went to a mountain in a preexisting world and it was huge. had like 7 caves.