If we have a ground thaw, do you think I could plant some cloves now?
It might work, worth putting a couple of cloves in the ground to see. Garlic seems to like to be watered but not wet, if that makes any sense. A really damp spot is bad, needs to dry out between rains. WikiHow has a good tutorial:
http://www.wikihow.com/Grow-Garlic
You can also apparently grow it indoors, just do a web search.