I noticed some of my seedlings (specifically eggplant, and okra) are having trouble due to a few cold days, so I'm wondering how hard it is for seedlings to bounce back after being transplanted from their grow pots to the garden.
Fruiting garden plants:
If they survives, they will grow again. Just with more delay. Eventually you should remove existing fruits (or the next fruits). Often you can eat them (but not with standard recipes).
Other plants (greens):
The cold may get them the trigger: winter is coming (and passed), so they may skip the first year growth (so good taste), and directly go to the second year: so flower and less green.
Unfortunately you can not do much now, but waiting. Mulch and humidity could help for short cold period. A transparent plastic sheet could also help for the first periods (or as emergency measure). If you have a green house, keeping them in pots helps to have early harvest (and larger plants, so less prone to be killed by slugs).
Young okra can be damaged by non-freezing cold temperatures, much as watermelon. However, it's not a sure thing that only a few days of cold will kill them (it might set them back and/or stunt them for a while), and it might impact germination, but I'm guessing they'll live. You might want to give them some phosphorus (it's said to help with cold tolerance, and plants tend to show deficiencies in phosphorus when it gets cold; I usually need to give my plants phosphorus in my unheated greenhouse if I use a seed-starting mix).
Eggplant should be fine, I'm guessing. It seems slightly more tolerant of cold than tomatoes, and tomatoes are usually fine (although some breeds of tomatoes definitely do better in the cold than others, and the same is probably true for eggplant). I've never had problems with eggplant in my unheated greenhouse. I have had problems with okra, though (and although it can initially sprout fast in the greenhouse, the cold can stunt or kill it—the cold can also inhibit germination).