Having said that, context will often be the ultimate factor. At Chanticleer we cut and mow down much of the fading vegetation, leaving some grasses (which are dealt with in late winter/early spring), and evergreen perennials. This is primarily because we have to get the garden ready for spring before the winter starts to set in and while we have the staff on hand. If we waited until spring, there would be too much to do to get ready for opening. Plus we don't know how cooperative the weather will be at that time. This year there was snow on the ground when we arrived back, which won't work for doing cutbacks! So you have to decide what works for your situation.
Seed pods of Abelmoschus manihot
Sunset by the ponds
Hystrix patula aka "Bottlebrush Grass"
Polystichum acrostichoides is left uncut (here under American Beech)
Sporobolus heterolepis is left to be burned in late winter