There's apparently a word for it:
Marmotomancy - Divination by groundhog

While reading Honest Wagner, I stumbled across this site, and found the word marmotomancy, which frankly is an awesome word. If I ever decide to try to customize out my own version of Nethack, marmotomancers are coming in as a low-level monster. It then occurred to me that there might be one thing that unifies Pennsylvania, the Groundhog. Even the PA Lottery, which can't do anything right in their ads, notices this, with their ads featuring Gus the second-most-famous groundhog in Pennsylvania. For some reason I then turned my thoughts to the notion that their should have been a military unit from Pennsylvania nicknamed the Groundhogs. Not sure why my brain made this leap, but it seemed cool. Some sort of marines, or mechanical infantry with the logo of a groundhog at the wheel, with the slogan "Drivin' Angry". So I did a search for "groundhog army" and found this on one link, which makes me feel a little better. Then I saw this. I don't feel so good about it now.