I'm wondering what to do about our pool. It is warm enough here in SC that we don't need to close it, but we are getting a ton of debris in the pool--so much that it is far more work now than it was in the summer. With all the rain we've been having, the skimmer gets overwhelmed quickly, and the bottom gets covered with leaves and pine needles. We managed to clog the return lines while vacuuming last week.

I would prefer to avoid that in the future.
Boy, I'm with you there on leaves and debris. I've been battling since '86, and yes it is a lot of work. I have to babysit the pool the whole time the pump is on. A really good inexpensive tool for removing leaves is a leaf eater. It has a big bag. You attach a hose to it and the venturi action sucks the leaves up into the bag. You can, also, get different size bags and different mesh sizes. When I let my pool go for a couple of days I'll use that to get the majority of leaves out before turning Polaris 280 on to get the rest (I have to change the Polaris bags out several times a day, empty the PoolSkim bags twice a day or more, and clean out the skimmer several times a day, on heavy days. BTW... I have two (2) PoolSkims that capture a whole lot of the floating leaves before they get to the skimmer but many still do get to skimmer if there is a lot of wind. If you want to go the vacuum route you really need a leaf catcher canister on the vacuum line. It will catch all of the leaves before it goes into your lines or pump basket.
Part of the problem may be that the deciduous trees drop there leaves over a much longer period than up north. Maybe this high maintenance period will end shortly. Is that possible?
Same here. Leaves are still dropping and blowing around and into pool. I don't have the lawn crew come out to take care of leaves until mid January because leaves are still dropping. It's been especially heavy past few days.
We're looking at leaf nets as a possible way to keep all the junk out of the pools. Do they even work?
Yes, they do work well for leaves and large debris. Not sure about pine needles but after you get a layer of damp, soggy leaves on net some needles should be stopped. During dry times the leaves will dry up and blow off of the net if you have enough wind. I've used one a few winters BUT you have to be very careful to block the pool off from any pets, including cats. I haven't had any squirrels drown though. It basically floats on the top of the water and keeps leaves out but not any smaller blowing debris. It does make spring cleanup fast and easy especially if you take it off with two people folding it back on itself to capture the leaves. Actually, I've always done it myself with almost no leaves falling into pool. I secured mine with large concrete blocks and large planters to keep the dogs from getting to the pool edge.
What to you southerners do with your pools in the winter?