What you got at Kroger's is probably a softneck variety. Here in Ohio, for me at least, I find that hardneck varieties grow best. I especially like the fact that hardneck garlic usually has only 6-10 LARGE cloves per head, depending on variety, much easier and faster to chop. Some of my garlic heads almost equal the size of my fist.
Hardneck garlic does best where there are hard freezes, they need to go dormant, but not really. There was a book written a bunch of years ago, I forgot the title and the full name of the author, but I believe the last name was England. He documented that garlic did indeed grow when temps were below freezing.
I don't know where in Ohio you're located, but if you have any active farmer's markets going, go see if any are selling any hardneck garlic, it's not too late to plant.