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.