Super interesting to me. Because I live in a town of ~13k, I would have said 10-15 is the cutoff. Just interesting to see what different people think of as "small". Cheers!
I would not try to put a number on it. Some towns just look and feel smaller, or larger, than the census count might indicate.
One way I know when I am in a small town is when I'm taking photos and someone asks me, "How yah all doin'?" (That's the way we talk in the Ozarks.) In the local vernacular, that is part greeting (small town friendliness), part curiosity (small town nosiness), and part challenge (you don't look like you are from around here, so what are you up to?). In the bigger towns and cities nobody pays much attention to the weird guy with the camera.