We found some (2 veins) silver on a tiny slice of mountain on our first island, which was a big surprise for me because I heard those tiny ones usually don't have any. Both were guarded by a Stone Golem.

Make sure you have your wishbone equipped and watch for the coloured rays around your character as you explore if you have music on--otherwise you'll hear the pings easily.

If none of that applies to your situation, I'm surprised to hear that a larger mountain biome would lack silver veins. Extremely bad luck, perhaps? Do you know of other mountains you can try?