A hog is a large animal, bigger and traditionally more ornery than a pig.
A hog on ice cannot manage its own affairs - its hooves get no grip, its legs are not agile in the proper way, it is as likely to injure itself trying to walk as maintain its footing. And it got there on its own, somehow - sheer cussedness was likely involved.
Also, a hog on ice is very difficult to manage - you can't steer it, entice it, etc, it's unlikely to be in a cooperative mood, it's big and strong and likely to injure anyone trying to help as well as itself.
Independent, see, of everything - sense, persuasion, authority, its own guidance as well as anyone else's.