I live in deep South AR, right on the LA line, we do get some nights down to around 20 but they are few and far between wtih the day temps usually rising above freezing afterwards. Do I need to do all of the steps for winterizing or can I just clean, algae shock, and cover? Will I still need to run the pump and sand filter, or should I buy a skimmer cover and leave it off for the winter?

You might not want to winterize at all. As long as you have the pump running any time it is below freezing you should be fine. Doing a minimal closing, as you describe, is actually more of a risk. That will work many years, but now and then, when it is cold on an unusual number of consecutive days, you can have plumbing damage.

I'm about 100 miles or so dead south of you and I made it last winter with pool open-----------in spite of that freakish 4 day period when it NEVER went above freezing. Run the pump, run the pump, run the pump! Did I mention run the pump?
Better if you cover the equipment pad to break wind and keep freezing rain off stuff. I am hard pvc plumbed and wrapped mobile home style electrical heating tape with foam insulation foil backed taped around it. Other tips include a plywood box around the equipment with a 100 watt bulb on a drop light cord. You get the idea. If leaves are a problem like mine are, they can clog a skimmer basket in about 15 seconds. I rigged a mesh vegetable sink strainer basket in front of my skimmer with aluminum wire so I can run the pump while freezing or any other time without worrying about starving the pump and still filter. Gonna use that next week while I'm headed to Vegas too. My luck, everything will decide to start dropping next week. Your only other concern is a loss of power to run the pump during bad weather outages. Best excuse I could find to buy "HER" a generator!

So do I only run the pump when it gets to freezing temps and no other time? Also, do I still need to put a solid cover over the pool or just a leaf net? Will I still need to vaccum in the winter? Sorry for all the questions.

Once the water goes below 50 degrees you don't really need to run the pump much at all (unless it is below freezing). Most people like to run the pump for perhaps an hour a day just to help skim debris out of the pool. If you go this route there is no point in using a solid cover. Some people like to use a leaf net, but personally I find manual skimming as needed easier to deal with than a leaf net. You don't generally need to vacuum while the water is cold.

All the above being said - I generally treat the water, put in a gizmo in the strainer, cover the pool, remove the ladder and handrail, and drain all my above ground pool equipment. And I like to do it BEFORE the leaves start falling. I'll keep the pool open as long as the pool water is above 70 and there is a chance of the air temp being warm enough to justify a swim (75 or better - and yes - October gets that quite often here). I took a swim yesterday (my birthday ) like I try to do every year assuming the pool and air temps cooperate.

I'm in North Florida and I have always taken care of the pool like I did during the summer, except as the temperature drops I would lower the number of hours the pump ran per day. If it was supposed to freeze that night I would run it all night. Having a timer helps to make it easy. Otherwise there were several days when I would just run the pump for two hours. Chlorine usage also goes down dramatically. I like having the ability to dump water out using the pump if it rains a lot and the water level gets high. I also liked having the circulation if I needed to add chlorine.

The only problem I have had is this spring I had a leak and couldn't tell where. It ended up being the pvc pipe fitting leading from the filter into the pool. The part on the outside next to the wall. The fitting had cracked. I was told that with the winds we had that winter that there were a lot of them cracking. Not such a bad crack to really see, but bad enough to cause the water loss. So even though I ran the pump on the freezing nights and protected most of it, the wind chill nights got me. I am going to cover that part this winter.

im from south ark also, first time pool owner, if i keep my pool open this winter, is there anything to watch for when its cold, like the ph going up, etc ?

If you keep it open the you still have to perform regular maintenance just like you do now, only not quite as often. You'll also need to ensure your pump runs whenever it's going to be below freezing if you don't have a timer with freeze protection. I find it easier to winterize and not worry about it for a few months.

I have a SWG on my pool. What if anything would you do differently if you were to keep the pool open and just run the pump on days when it is freezing? Right now I run the pump 24/7 and my SWG about 6 hours a day. From some reading I have done today it looks like I need to get a timer and just run the pump a few hours a day instead.

There are a few of things you'll need to do that you don't normally do. Run the pump an hour or two a day. Since your swcg will most likely shut down at around 60º you'll need to manually dose chlorine once in a while. You'll also have to make sure your pump runs whenever it's predicted to freeze.

So I could just pull the SWG out and store it for the winter at some point then. Can Clorox be substituted for chlorine? or is chlorine the better choice.

No need to remove the SWG. I would test to see if it is producing chlorine and use it as long as I could.

Then, when the water is too cold, switch to chlorine. Bleach and liquid chlorine are identical in every way except for strength. Good bleach is usually 6% and liquid chlorine is usually 10-12%

Dave said what Dave would have said. I think you'll find that you don't have to use very much bleach during the winter.