Acorn Squash Skin...
Hmmm...interesting question...some say it's inedible but I roasted an acorn squash cut into eighths last weekend rubbed with olive oil, salt and freshly ground black pepper @ 425 for about 20 minutes...loved it so much that I DID eat it with the skin and it did not kill me...eating the skin was rather inconsequential to the flavor and I loved it so much that I bought another acorn squash tonight that I hope to roast tomorrow to include in our Thanksgiving feast. Just my 2 cents!
One way of eating acorn squash is to bake the halves, or large pieces. Then season them (butter, brown sugar etc), and let the guests scoop out the flesh.
Some other squashes have a thinner skin that can be eaten. Japanese recipes often call for peeling the skin in stips, for decorative purposes, and to leave as much flavor. The skin will still be harder than the flesh, so not everyone likes it, even in the thin skin versions.
So for some squashes peeling, before or after cooking is a necessity. For others it's a matter of taste.