I subscribe to the idea of cleaning up the garden in the fall, so i won't have to do it the following the spring.
If it's brown, cut it down.
If it's green, it's clean.
Oftentimes, though, the body just doesn't keep up with what the mind has planned for it, so when the first snow falls, i notice various tall brown stems sticking out of the snow. "Hmmm," i think. The mind gets busy again, trying to bend the body to its will. "I should go out there in the freezing cold and cut those down."
A few dead plants actually look good in the winter garden. One is a tall grass, variegated green and white in summer, and now tan with a thin layer of snow. The leaves rustle gracefully in the breeze, and the seed plumes wave.
My friend Frances left her Autumn Joy sedum standing on purpose--the flowerheads retaining a bit of the maroon color. Now an inch of snow sits atop each flowerhead, making them look as if they've bloomed again, and bringing Frances winter joy.