I do both, cut some down that are in the way or just to tidy up but if they are doing no harm I leave them. Mine have survived -18c 2 winters ago. and I have seedling popping up all over the garden. They do seem to seed in between crack and on gravel. I would leave the seed heads on this year and you will more or less guarantee seedlings next year.
A lot of my garden is fairly sheltered so perhaps that helps.
I have given them away to friends and relations and all from 1 original plant.
Chris.