Looking back at the amount of snowfall I saw as a kid and the amount of snowfall I see now in my 30s, or at the number of hot summer days ... I find it hard to claim that climate is not changing over a lifetime. 20 years isn't even a lifetime, that's like 1/4th of a lifetime
Maybe climate is more stable wherever you live
There's a problem with memories. You can have a snowy week and remember it as the entire winter, if it affected you in particularly memorable ways. Kids usually get out of school and play building snowmen and having snowball fights.
When I was a kid in the midwest USA, 100 degrees in the summer happened every once in a while. Still does. July and August were always hot. Still are. As a kid the heat didn't bother me so much, I'd go out and play in the sprinkler or go to the pool. Now, I've got to wear clothes and work. Makes the heat more noticable.