I went without covering last year (my first winter), doing the same this winter. Like you I waited, a bit too long last year (see below), till the water was cold. Then I disconnected and drained the pool a bit, and left it all winter.
Here it is in January 2021:
Here it is March 13th, first day the last of the ice melted.
March 16th, got some pool lights, testing them. Starting to see a hint of green.
March 20th, I wake up this Saturday, see this, and realize I need to open the pool NOW or I'm going to have a long SLAM ahead of me.
March 20th, a few hours later. I had added a couple gallons of chlorine, then brushed a bit to mix, and netted out most of the leaves. Then I started filling while setting up my pump and filter (now visible off to the left side of the pool).
Hopefully this helps you. My key takaway is once the pool fully melts, without a cover you need to get it open ASAP, cause the debris and sunlight will cause algea to start growing. On the flipside from the time I closed to the time I opened I paid zero attention to the pool. No need to buy/install/check/drain a cover.
Also as you can see when caught early the little algea I vanish immediately. You can see in the pics how in a matter of like 3-4 hours the pool went from green to blue. Caught early, with cold water, easy to manage. I suspect your dad had issues without a cover because it was not caught early when the water was cold, so it was a fight to clear the water.
Oh yeah. The water will be the 5 day or so average temp. At freezing it only needs to move a little. The colder it gets the more it needs to move. Niagara Falls for example has never froze in known history.
From closing too late last year, I'd like to point out that moving water not freezing is a myth. I would say the reason certain moving rivers and waterfalls do not freeze is because they are churning up water in contact with ground below the frost line, i.e. not frozen, so it keeps the water from freezing.
If your water is well circulated such that it's all the same temp and if the temp of that water gets to 32 °F, it WILL begin to freeze, even inside pipes with moving water. This is what happened with me last year. Kept my pump running 24/7, fine through freezing nights while the water was above 32, finally waited long enough we had a cold spell starting where it wouldn't even get above 32 in the day, water got down to 32, ice formed over the pool surface. Went out and pump was struggling to pump water. Started disconnecting hoses from the pump and they had ice building up inside them. Put the disconnected hoses on the ground to drain water out of the pool by gravity and the pipes froze up and stopped draining. I managed to get the pool drained enough by punching through the ice and using a submersible pump and garden hose to drain the pool. Then I had to drag my sand filter inside cause it didn't have time to drain and the temp wouldn't get above freezing that day.
Bottom line is you're fine going below freezing if the pump is running (and you don't loose power), AND the water temp is high enough above freezing it won't hit freezing overnight. But if the water temp is getting close to freezing, GET IT WINTERIZED ASAP before you hit that mark!