I have studied the history of mining for a long time, and I have never run into this assertion. There are stories that link a prospector's discovery of gold or silver to the wandering of a burrow, and the prospector having to chase the creature, which leads to the accidental discovery of an ore body. But I never heard of any assertion that the burrow knew where it was going or that it could detect any mineralization through smell or anything else. This kind of wandering burrow is the basis of the Tonopah, Nevada Silver strike. It also has an odd parallel with Mary Leakey's discovery of an important hominid fossil while an chasing errant dog.

This sounds like an urban legend. If animals really could detect minerals like this we would be up to our eyeballs right now in gold sniffing dogs. When dogs are tracking they follow a trail of shed organic matter. Gold and Silver don't shed a trail of organic matter in fact they don't shed much at all without a good amount of friction. Further dogs often lose the trail when crossing streams or rivers because the particles become trapped in the water. If you don't understand the problem there I suggest you stick your nose underwater and breath deeply to get a good smell. Underwater, dogs and humans have about the same smelling ability.

Now there is a small chance that this is true for a completely different reason. Gold is found in rivers because it washes down from veins upstream. The gold tends to settle in bends in the river where the water becomes calmer. Horses and other animals like these kind of places for drinking. Running water tends to have less harmful bacteria than stagnant water. But running water also contains suspended solids like dirt and gold. These solids fall to the riverbed at calm bends in the river and this gives animals a place to drink clean water. To an extent this would cause horses if left unguided to naturally gravitate toward good places for panning gold. On the other hand an experienced prospector would be able to spot the places better than a horse which makes it unlikely this method was used much if at all.

This is fake(the person was obviously telling a joke).

Silver has no smell, and there's no silver dust in the air anyhow since it's very dense and would not be floating in the air for animals to pick up, nor is there any evolutionary/biological reason for horses to be able to detect silver.