I let it go. On very cold days, you will notice that birds look rounded and chubby. Birds also move into protected areas out of the wind, and stay out of water that might freeze around them. You were kind to give the bird seed and water. When everthing is frozen, they can get thirsty.
Many birds appreciate suet in the wintertime, in addition to seed.
That's why it's important, if you start feeding birds in the fall and early winter, to make a commitment to keep feeding all the way until spring, when food becomes abundant again. Groundhogs A groundhog has taken residence under the neighbor's shed behind our garage. I thought they only ate plants. Since my other neighbor moved with her cats, we miss the mousers. Groundhogs are really exclusively herbivores.