The apples are about the size of a quarter now, and a good many of them have dropped off the tree. Is that normal? My chickens seem to have no interest in eating the fruit drops though

The call it "June drop." Means you have less hand-thinning to do. Right on time.

Great! Should I clean them up though?

Yes, to break codling moth reproductive cycle. Check for codling moth "stings." (good picture on link).
You may want to thin more yet, depending on how good a fruit set you had.

We are not having that problem after our drop below 20 degF this spring.

Oh yeah, pretty sure most/all of my fruits have that sting mark.