Even when the beaches froze solid in Maine, we just switched digging tools from shovels to hatchets and masons hammers. My buddy completely wore down a brand new Estwing hatchet one winter, but I had better luck with the masons hammer. Oh, we would cut a silver coin in two now and then, but we kept going. It really sucked when I would be hacking out a plug and get a load of frozen beach sand right in the eyes. I just sit down and cover my face until the sand thawed, get it all out and then go back to digging. All that just to find a penny!
Ya gotta love it!
Good luck!