In addition to finding this question when looking into this, I came across an article from the University of Illinois Extension, which had some relevant information:
Probably the concern over eating produce after a freeze goes back to one plant – rhubarb. [...] We eat the rhubarb stalks and should never eat the large leaves any time of year. The leaves are inedible because of oxalic acid and oxalate content which can cause poisoning.
In response to low temperatures, oxalic acid increases in rhubarb stalks as leaf tissues begin to freeze.
This is given alongside advice that frostbitten tomatoes should not be canned due to potential bacterial infiltration (made possible by the cold-damage) plus what the the Montana State University Extension's Lynn Paul says:
Frost bitten tomatoes have less acid in them, which is needed to keep the food safe during long storage after canning.
Otherwise, resources I found seem to agree with the other answers here that frostbitten vegetables in general are safe. I'll update this answer if I find other caveats.