If you don't get a lot of freezes at night in the winter, you may be happier maintaining it. A lot of folks in AZ and other southern locales keep the pool open and running year round. During the winter, I shift my pump runtime to late-night, and if there is a freeze watch/warning, I set the pump to run constantly until the temperature warms back up (very rare in Tucson, maybe more common in Texas). Chlorine consumption goes way down when the water is cold, which requires less oversight (I tended to test weekly this last winter), so it's a personal decision you have to make.
Also that is not a binary choice. I have closed for some winters and kept it going for others and I have never slammed my pool. The key is to close late and open early if you do shut it down for the winter.
From Oct 1 till now I am at 6 to 7 gallons of 10% bleach used. Very easy to keep levels up my first winter I was adding once a week now with the Stener I don't even have to do that. So as triptyx said freeze would probably be your only concern, it takes a lot more to freeze than many think.
So other than having to keep the leaves out of it, you could certainly keep it open if you wanted. As mentioned above, closing the pool early enough, then opening sooner before the water has a chance to warm up would likely require less SLAMming.