To a lot of the general public it actually doesn not count in their eyes. I've had many storms just over the past 5 years where i got 6" or more under a winter storm warning and all the roads were wet, especially the highways. Most people i've talked to think the forecast busted because they only had to plow a sloppy inch off their drive or sidewalks. To some extent i can agree with them.
I really think winter storm warnings and advisories should be based on impact and not just an exact snowfall criteria measured on a white reflective surface cleared every six hours perfectly placed. Even with general forecast from the private sector or news stations, when there is a substanial difference i think there should be two maps, one for roads/sidewalks/highways and one for grass/decks/roofs/wood etc. The former is what has the real impact, not the latter. Or they can at least mention and emphasize the difference in accumulation on different surfaces.
I don't know what the right answer is, just throwing this out there. I do know the vast majority of the public (from my social circle. family/friends/etc) has no idea what the difference between a Watch, Warning and Advisory is. All they want to know is how much and when.