I like to leave them on, they look pretty when there's a frost. If you want to remove them, just cut them off.

Same here but not only with hosta. Leaving stems on is a good way to tell the plant's location in the spring when you want to do other plantings nearby. Keeps you from inadvertently digging up roots, bulbs, and rhizomes or seeding over existing plantings.

If you don't want the hosta putting energy into producing seed then there's nothing to stop you cutting the flower stalks. I tend to leave them until they've dried off and cut in the dry length so that there isn't green material at the cut.
My hostas are all in pots so I don't need a reminder of where they are.