I guess no one has bluegills here to advise you.
I imagine you would treat them the same as koi,
but really that's just a guess.

Are bluegills considered cold water fish, like trout? I saw our local hatchery posted that they were out feeding their trout in the -15 degree weather. Someone asked why they feed them in the cold unlike koi and goldfish that we stop feeding below 50 degrees and they explained that trout are cold water fish and need to eat all winter.

Don't know if that helps at all!

They are native to Oklahoma, therefore cold tolerant. What I don't know is whether they need supplemental feeding in a new, small pond that has not had time to become rich with invertebrate food sources. I have had one in an established pond for several years, and it is happy. Thanks for the input!

I have two in my garden pond along with goldfish and others and they have been there now about 4 years and they do fine. I stop feeding during the winter months.

Take a clue from nature, Bluegill and other fish including Koi and Goldfish will eat in cold water if food is available like in a mud pond, lake or whatever and if the fish wants to eat.

The thing about not feeding Koi and Goldfish when water is less than some temp is more like your Mom saying you can't swim for an hour after eating or you'll die in the water. Mom is trying to get some result without having to debate the topic. Death is the king of hyperbole.

Fish eat less in cold water no matter if cold or warm water fish. People dumping loads of uneaten food into a pond increases the load of Aeromonas bacteria which increases the risk to fish because in cold water their immune system is very low.

But all that is way more info most pond keepers want to hear so we just say "don't feed fish under 55F or the food will rot in there belly and the they will die". In warmer water we say "Goldfish will eat until they explode and die so don't feed them too much". Invented to scare people who aren't really interested in the details to reduce waste in a pond or tank.

So for the Bluegill if you understand about the need for keeping water clean you can certainly feed them. Whether they eat or not or how much is up to them. However, if you don't understand how food and bacteria relate to poor water and how poor water can kill fish, don't test water, etc., then not feeding fish at all will probably give the fish a better chance at living longer. Not super long as poor water and nutrition will get them someday.

Using death as hyperbole is very effective for Moms, marketing departments and online.