There's nothing figurative about this tweet. It is about as literal as possible. "Mourning doves" are a specific kind of bird (the picture with a tweet shows mourning doves - https://ru.wikipedia.org/wiki/Плачущая_горлица). The reason they're called that is that they make a sound like someone crying; regular doves look and sound different. When you squat down and curl into a ball in order to stay warm, it can be called "hunkering down." That's what the birds in the picture are doing. \

A Mourning Dove is the type of dove that she is referring to. Hunker down is a verb. In the example you gave it refers to “being still” or “staying in place” as animals and people do when it is cold outside. Another example would be: A storm is coming so we’re just going to hunker down and ride it out! This is a common expression in the United States. Hope that helps you. :)