@jseyfert3 leaves his uncovered & deals with snow/ice
I did, but this is our first winter with the pool. I may consider doing at least a mesh leaf cover next winter, if not a full cover.
Note due to leaves I kept my pool open at late as possible so the skimmer could run and I could vacuum. This was until the water started freezing (okay, I kept it open a
tad too long). This was like November, and we didn't swim hardly at all in September, if at all. So it was certainly extra work. And probably due to the combo of leaves in the pool and lots of light from being uncovered I did start getting a green tint in the fall during a warmer spell when the water temp was still "too cold for algae" and again this spring.
Here is my pool March 13th, the first day it had no ice this year.
And here it is Saturday the 20th, water temp at 50 °F.
Finally here it was again also on Saturday later in the afternoon, after adding chlorine and scooping out some leaves.
I'm assuming a cover would have helped slow some of the algae (BUT IT WILL NOT STOP IT), and some Polyquat 60 algaecide would also have helped (I did not add any when closing, though I plan to next year).
You can certainly uncover and let rainwater fill, but keep in mind you will likely need to add chlorine if it's two months till you open. And adding chlorine without a pump means lots of manual brushing to mix it in, though a submersible pump or similar could be used to circulate the water and mix it in too.
Note in my last picture I was filling. Given it was going green, I figured I'd open it now. I filled just enough for the pump to work. I'll probably run a low number of hours per day just to get some skimming and make sure it's all mixed up for when I add chlorine or test.