I think all those requests may have overwhelmed our trusty Winter Bash servers in one way or the other. I have disabled hats for anonymous visitors on Stack Overflow to cut down the traffic a couple of hours ago, and everything seems to have been fine since. I'll enable it again once the CDN configuration is correct, and monitor further.
If somebody was seeing issues very recently (at the time that I write this answer), that was something different -- the first attempt at fixing the CDN config was more of a Verschlimmbesserung (and was quickly reverted, but since it involved a DNS change, you might still see some blips).
Update: Should be all good now.