Nick, the 60-degree threshold is a guideline, not a hard cutoff. The real number that matters for algae is closer to 50 degrees - below that, most algae strains essentially go dormant. At 62 you're in a gray zone, but like Sarah said, the chemistry has to stay active. The thing people miss is that the bather load drops off so they stop testing as often, then they get a surprise when they finally go to close.
If the kids are still getting in a few times a week, keep your FC in the upper range of whatever your CYA demands and test twice a week minimum. Phosphate levels creeping up during the shoulder season is a real thing too, especially with leaves starting to drop, so keep an eye on that. One thing I'd actually watch more than algae is your equipment. Running the pump in colder weather isn't the issue, but if you're in a part of NC that could see a surprise freeze overnight, you want to be ready to close on short notice rather than scrambling.
My personal habit in a similar climate was to set a firm mental deadline - something like "if we hit two consecutive nights below 38 degrees, we close that weekend regardless of who wants to swim." Takes the debate out of it and gives you time to get the chemicals right before closing rather than dumping everything in last minute.