After Halloween, I put our pumpkins on the stone wall out back. The squirrels gnaw through the flesh to the seeds. I also give them the Indian corn I used for decoration. When I make applesauce, I put the cores and peelings out for them and other species that might be interested. I never put out a lot at once and never near the house.
Squirrels do eat birds' eggs as part of their natural diet.
This makes me pause. I help the squirrels in rough weather, but I don't want to support a larger population than would naturally occur in our habitat conditions. Not wishing to start a cascade of consequences that I might never know about, I limit my interference. Enhancing the backyard habitat with plantings, nest boxes and water, with a few feeders to supplement natural food sources, is a less precarious way of benefiting wildlife generally. It avoids the disadvantages of excessive feeding, such as attracting large numbers of starlings, English sparrows, and pigeons as well as squirrels.