For example, I found this profile, where the person is covered with a hat all over his avatar. Can I somehow see the real image behind?
Just execute the following code in the developer tools of your browser:
This is the result on your profile page:
I don't know if there's something inside SE that does it, but you can do it with the browser inspector.
- Open the browser inspector (CTRL+Shift+I on Firefox at least)
- select the "select" tool;
- hover over the hat until a "rectangle" appears around it. Click on said rectangle;
- Remove it with the Delete key.
The hat is just a SVG positioned on top of the profile image, the actual avatar isn't modified. So if you're using Chrome, you can go to their profile page, then right-click somewhere on their profile picture that isn't the hat, and select "Open Image in New Tab" to see it without any overlays.
Since Winter Bash is not supported on mobile theme, just click the "mobile" link in the footer of the desired profile page, and you will see the avatar in its full glory.
You can then click "full site" to resume Winter Bash as usual.