I think in my game we have explored about 70% of the map.. we have like 6-8 mountain biomes.. and have located 5 caves.. they seem to be rather rare.. I do not think we got enough materials IF we all wanted lets say fenris armor we could not make it.. maybe enough for 3 of us. Maybe our seed has bad RNG.

caves got walls you can knock down. A totally empty one is unusual. Not impossible, but double check it.
Caves are a little rare. If you had seen the mountain before the caves were released, none will spawn there (old world?).
Otherwise keep trying. Thankfully you don't need too many of them to get all you would need from them. I think 5 or so should get you enough for 1 person with any luck.

its a bad feature but the current design. fenris hair discovery rate is really inconsistent.

RNG. Not all mountains have caves. Not all caves are impressive.

Keep searching.