My family took a vacation in January (yay!) and came back on January 29th to see some of the garlic already an inch or more above ground. The warm mid-January weather usually does that. There have been very few winters where cold and snow has kept the garlic from popping up in late January.
The garlics that were up are the "Turban" types (Tzan, Shantung, Uzbek Turban and Thai Purple). These garlics are always up first and they get harvested first, too, in mid-June.
Cold February kept the garlic from growing any more, and the tips are still about the same, with just a few of the other garlics barely visible. The snow helped protect the garlic for a while, but of course it got windy and dry and now the tips are a bit naked. A little mulch would have protected these tips from the harsh climate, but it's too darned windy here for us to mulch our huge garlic beds. Anyhow, I know from experience that everything will be fine, and as soon as it warms up a bit (tomorrow?) the garlic will continue to grow and the weather-beaten tips won't affect the growth. The cold nights are fine for the garlic, even with the tips above ground, although it would probably do a bit better without the extra challenges they face.
With the winds, and the warmer temps on the way we'll be planning to water all the garlic beds soon. Now is a crucial time for them to stay moist.