Ah, so it's a call-back to one of Agnes's lines from the movie. And based on the tweet, it seems I'm far from the only one who didn't get the reference. :-)
While I think you're definitely onto something, the ones I'm seeing when I look it up have more brown on them and don't seem to be mostly white. I don't doubt you though.
Yup, a ptarmigan. The plumage around their feet becomes especially thick in winter, and their claws grow in length, basically giving them nice little snowshoes.
