Gardeners, apparently, come in one of two forms: the Oscar Madisons, who leave everything standing in their gardens, even after the first frost. They like the idea of providing food, cover, and habitat for the little wild things in their years.
Felix Ungers, on the other hand, clear everything out of the garden and leave everything spick and span, satisfied they've not given any bad insect or plant diseases a place to overwinter.
So what should your approach be?