shire

It depends on the species and on how dry the soil in their pots is. It
is possible to keep eg Opuntias outside all winter in S England if bone
dry.

If the freezing itself has done damage, I'd expect that to show up quite
quickly, but if they're damp as well it may well be not till spring that
you find out they've rotted off.

I don't think it'll be 'lasting damage' as such - they'll either survive
unscathed or die completely.

I'm not sure about this. Some cacti scar up and/or develop corky
scaly patches as a result of frost exposure. They survive but
its disfiguring.

Mesa gardens have some interesting books
http://www.mesagarden.com/books.html

And here's a page of species that withstand -30C in Finland
http://www.sci.fi/~cubase/hardycacti.html