No, no herbaceous perennials "need" to be cut down before the snow flies or later - no one cuts then down in nature at all; new stems just push up through old ones. (By the way, herbaceous perennials are those that largely die to the ground and go dormant for the winter.)
In a garden setting, it's completely up to the gardener whether to cut off old stems in fall or spring - which is done mainly for aesthetics only. It makes absolutely no difference to the plant whether dead stems are cut off in spring or fall - they're dead either way. Here, where we have thin and intermittent snow cover, I leave everything stand until spring, in order to have something to look at. As well, birds feed on the seeds, and the stems help to catch and hold a bit of snow. Where you are, in a heavy snow area, it may be that your plants get packed down anyway? At any rate, it's completely up to you, and it has no effect on the plant.
I agree.Call it natures mulch.Its easier to locate plants in the spring.If you tidy up to much its difficult to remember where your plants are located.I can remember years ago,I would totally remove all the dead.In the spring when the new shoots came up rabbits ate all my tender new shoots.By leaving some of old dead it protected them.This was true for my purple coneflowers.By leaving the old woody stems,the rabbits did not have easy access to the new growth.