Maybe we have a bad recollection of the winter as it was when we were children? Maybe we enjoyed so much the short time while we had snow that it seemed like the whole winter was snowy.
I know, I have thought about that too, but I didn't use only my memories, I used adults memories as well. And here in the US people say the same thing, it used to be more snow in the 70s or 80s. That confirmed that it was not my small height at that time or, as you said, the mind of a child, it was in fact more snow.
What you suggested as a problem, is in fact what probably makes me feel that things are worse now. It snowed Friday night, and then is was so sunny and warm Saturday that almost all the snow melted. And when I think that I've been told this was supposed to be one of the worst winters in the past couple of years...

I didn't get to build the snowman I wanted to build this year, this is my main problem.

Will I get the chance to do it, only time can tell. I'll keep you posted.
