If you planted Garlic early this fall in anticipation of a spring harvest you may have noticed that it has already sprung up. In all but the coldest of regions such as Canada and the very Northernmost USA it will do just fine all winter long. Come the warm weather again in spring, say March or April, it will begin to perk up. Full maturity should be mid to late summer.
Some folks like to mulch the Garlic to protect it from the ravages of Old man winter, it's not absolutely 100% necessary unless you are in the harshest of environments but it is advisable.
At the end of Autumn into winter as the weather gets colder the top growth will slow down and eventually stop, the green stalks above the soil surface may endure some damage but generally not enough to seriously hurt the main plant.
A healthy layer of mulch will give your plants a jump start once the season begins in earnest. As well - you never known what mother nature has in store for you this winter, so if you feel the urge to mulch, go for it. Leave the mulch in place well into the spring to conserves moisture and suppress weeds. Garlic is ill equipped to compete with weeds.
Thank You and Happy Gardening.