The ones that grow in my mom's yard are perennial, but there may be annual or biennials varieties as well; I am not sure.

The roots of perennial thistles here in Europe grow very deep, they usually come back several times after being dug up.

The term thistle applies to so many different genera, it's hard to be very precise :-) Common thistles, Cirsium species, are perennials and biennials. Relying only on winter cold to kill off the plant is risky and unreliable. And most species are tap rooted as well, so digging out is a challenge.

The biennial ones spread by seed.
Assuming the frost/winter won't kill that.