Apparently a buried penny is a secret hat. I'm not sure what its criteria is. Also, is there a list of secret hats for this year's winter bash? Do the hats change every year?
2014 list: Winter Bash 2014 Secret Hats
Since Winter Bash is network-wide, it is not surprising that such a list is on Meta Stack Exchange rather than here. (Also the post which you linked in the question is on Meta Stack Exchange.)
I will also add a link to the Winter Bash 2021 chatroom - which is also mentioned in that question.