A first frost is not one event applied evenly to a garden. It sorts the beds into three groups: what a cover genuinely saves, what you should be harvesting instead, and what does not need you at all. Most of the wasted effort on a cold October evening comes from putting a crop in the wrong group.
The two temperatures
NC State extension draws the line at 31 to 33°F for frost, and below 26 to 31°F for a hard frost or freeze.1 Those few degrees decide almost everything that follows, which is why a forecast low of 32 and a forecast low of 27 call for completely different evenings.
Warm-season crops go first. Beans, corn, cantaloupe, cucumbers, eggplant, okra, southern peas, peppers, potatoes, squash, sweet potatoes, tomatoes and watermelon are all damaged in that first band.1 Alabama extension puts foliar damage on warm-season vegetables at 33°F.2
What does not need covering
Much of an autumn garden needs less from you than you would think, but the two lists here are not equally hardy and the difference is worth keeping. Broccoli, cabbage, cauliflower, chard, English peas, lettuce, mustard, onion, radishes and turnips tolerate a dip to hard freeze temperatures for a limited period, and NC State is careful to add that the foliage may still be damaged and the yield reduced.1 Brussels sprouts, beets, collards, kale, parsley and spinach carry no such qualifier: they survive extended periods below 26°F.1
If your beds are mostly that second list by October, the first frost is a weather event rather than a task.
What a cover actually buys
Alabama extension is specific about the size of the effect: loosely covering plants with a lightweight fabric such as a bed sheet adds 3 to 5 degrees to the ambient air temperature.2 That is a real margin on a 31°F night and beside the point on a 26°F one.
Three details decide whether you get those degrees. Cloth rather than plastic, because plastic transfers more heat and foliage touching it can freeze anyway. The cover reaching the ground and weighed down at the edges, because the goal is to trap heat coming up out of the soil rather than heat from the plant. And taking the cover off in the morning, because a covered plant in direct sun can cook.2
What to harvest instead
For the tender crops with fruit still on them, covering is often just a way of postponing the same decision by a few days. The tomatoes are the clearest case. Iowa State extension advises removing all mature, greenish white fruit from the vines just before the first frost, taking what is solid, firm and free of defects, then holding it somewhere cool and dark at 60 to 65°F to finish.3
The same logic covers basil and the other tender herbs, and the last peppers. A crop that will not ripen more fruit before the season closes is worth bringing in whole rather than defending outdoors.
The one thing worth checking first
All of this hangs on a date that is local and not obvious. A first frost in Nashville, in Atlanta, and in Mobile arrives weeks apart, and the average tells you when to start watching the forecast rather than which night to act.