Silver spawns when the mountain is tall enough. If you find obsidian and golems, then you are high enough to start looking for silver. Use the stagbreaker to thump the ground and look for Too Hard messages. This will show up for silver and for obsidian. So if you get that message and there's no obsidian next to you, then start digging.

Added: You will have a hard time mining the silver without an iron pickax though.