At a farm market this Spring I saw a display of garlic (hard-neck, if it matters) for sale that had started to sprout. The leaf-blades were at least an inch past the ends of the tip of the cloves and I wondered, would it still be possible to plant them and get any kind of harvest? It's still early Spring here with at least a few weeks of mostly cold days left, including a few freezing nights.
If you have sprouted garlic, don't hesitate to plant it. It's on sale because the culinary value of sprouted garlic is decreased and because it can't be stored longer. The cloves want to grow now.
Assuming your farmers market sells locally grown produce, I would assume the breed to match your local climate, so it should do reasonably well in your garden:
Cold/frost tolerance depends a lot on the breed, some are very hardy and get planted in late fall, similar to flower bulbs and are ready for harvest in late summer. Others (e.g. the mediterranean types) are less tolerant and are better planted in early spring, ready for harvest in the fall. This method typically yields smaler heads, but that's not crucial for small-scale home gardening, IMHO.
Follow the usual instructions (10 cm / 4 in apart, well-draining soil etc.) but be extra careful not to break off the sprouts when separating and planting the cloves. At this time of the year, you shouldn't need extra cold protection. If you want to add a cover like a foil tunnel it won't hurt, but unless you expect hard frost and a few feet of snow, your garlic should be fine.
I don't throw out my sprouted cloves from my kitchen stash - either they go in the garden or during the midst of winter, I stick them in pots, sometimes even as "subtenant" in other house plants, and harvest the greens. The latter method won't give me new bulbs, of course.
It will grow something. If you'd like to give it a whirl, do that.
It won't grow as much as if planted in the fall (personal experience doing it both ways - I have planted well into December on years I've gotten behind, because what I have gotten from spring planted garlic has always been pathetic.) A lot of important root development goes on over the winter in fall planted garlic.
Frost should not be a problem.
I planted my garlic out of season ( early spring ) and it did fine. I dug them up in late summer, and although the bulbs were a little small, I did get enough to make it worthwhile since locally grown organic garlic is so much more expensive then the imported stuff from China