Hi Glen -- I'm not sure why, but mine never seem to turn brown before our snow starts, so once fall is pretty well done I cut the stalks down regardless; I've had some problems with asparagus beetles and I've read that you should clean all the dead stuff out before winter as it can harbor the eggs or whatever. (We have pretty harsh winters where I'm at so I just have to do it when I can) For the same reason I always burn all the stalks instead of composting them. But other than the potential for harboring insect pests, I don't think there's a need to cut the stalks until spring.
Our asparagus is producing like crazy right now -- yum!!