That's how endless insects, ones genetically design to survive our winters, do so. They crawl under leaves and dying grass, which insulates them from the cold a bit. Their bodies can freeze and thaw, and they'll be fine.
If you watch robins in the spring, after the snow melts but before the ground thaws, you'll see them turning over leaves to find and eat the insects. I see a lot of this, because I have a lot of trees (rural property, with forest around me). Often there are robins migrating, who stop and fill up thanks to my lawn and its plentiful ground leaf cover.
As a child, I was taught that robins "eat worms". Well, they surely do. But I see them eating anything and everything which moves. They're a lot like chickens, I guess.
At dusk, I often see them standing around and catching moths and things which take flight. Leaping into the air and snapping them up. Fun to watch.
Robins only eat bugs and worms as part of their raising an egg and feeding the chicks. Once the chicks can feed themselves they all switch to fruit and seeds.