How soon should you remove frozen dead material from plant tops?

Basically, you are mulching, which is fine. Just make sure that the dead plant material is cut from the living plant so that there is not chance of rot. "Fluff" up the mulch material to get as much air in it as possible to help it compost properly. Depending on your climate, you can also add more mulch (purchased or extras from the yard) to help keep the roots of the live plants from freezing. And don't forget, the dormant plant should be watered once a month or so.

Hi Margie, It is fine but just remember that small critters might use it a home.

I like the 'contrast/texture' that many spent flowers/shrubs provide in the fall/winter months; just mulch well ( straw, raked leaves, even white pages of newpapers ) Not all plants are 'attractive' when defoliated ... cut those back, but don't waste the stems/foliage ... just lay on the ground or put in your compost pile for next year.

You can do that but i normally remove them after that first freeze and then make sure the plant i surrounded by a nice mulch.