This is something my parents did to me. I wore second hand clothes though, and God were they ugly. Checkered yellow and brown stretch pants. Snowpants when others were just wearing jeans.
The parka actually sounds nice. Can you stuff the other puffy one somewhere on your way to school? If you take a bus, you could "accidentally" leave it there and get it on the way home. You could keep losing them somewhere, like oops, I lost my coat cant find it, and I'm sure they'd tire of getting you a new one. Yeah, just start losing the stuff. It kind of made me smile to read this, my parents were to the extreme of overprotective too. Looking back, I know they just thought the cold weather would get me sick. Sounds like they need to realize that cold weather doesn't cause colds, get them informed on the internet? Best wishes