I hear this sentiment so much. Peoples memories really want to remember things for the best (or at least different than reality). The old timers always talk about the crazy winters we had in the 40's, 50's and 60's, however there is just no data to back it up. I think a lot of it has to do with how well we can handle snow now and predict snow these days compared to back then. A typical well forecasted storm now might have been crippling 50 years ago if it hit at the wrong time and couldn't be cleaned up well. I know that there are a lot of subtleties that I'm glazing over, but there just isn't historic data to back up the idea that winters used to be MUCH colder and snowier.
That said, there appears to be a small downward trend in snow amounts over the past 20 years (which I would be willing to bet has something to do with Anthropogenic Global Warming), but its barely statistically significant. Furthermore, if you graph snow totals in the ROC since 1940 you'll actually see our yearly snowfall average trending upwards (however this is somewhat skewed by very low numbers in the 40s). Anyway, there is a lot of data to digest out there, but not much points to winters being weaker now than they used to.