It would seem a lot of fun if it were possible to layer hats, some combinations would be hysterical!
It also doesn't seem possible to change the avatar for my profile during this time, or am I missing something?
You can't layer multiple hats through the UI provided by SE. However that doesn't prevent you from taking a screen shot of your avatar with a hat on, setting that as your new avatar and putting another hat on top of it. It's some work, but if you really really want to, you can.
I did a quick test and I was able to change my avatar, so I'm not sure why you can't.