Wintering over Herbs in an Unheated Garage in Zone 4-5

I grow herbs in pots of various sizes. Most are unglazed ceramic (terracotta?). I live in zone 4-5 (upstate NY). I know this is a premature question, but I want to plan ahead. I move the potted herbs into my unheated garage in the fall. They get minimal light. Thus far, the only herbs that survive and grow the next spring are regular garden chives but not garlic chives, tarragon, and mint. Given the conditions (unheated garage, minimal light), how can I optimize the chances for survival? I have given up on lavender, although it is my favorite of the herbs. I have a basement, which is warmer than the garage. Would they be better off there? What about watering?

The pots in the garage are not in the soil and the roots therefore get much colder than they would if grown in the ground. The temperatures experienced would be equivalent to almost two zones colder than if they were in the ground. To make them survive in your zone you can dig the pots into the soil and lift them out again in the spring, or keep them in a room that stays very close to freezing during the winter. The basement may be too warm. Chives and tarragon must freeze for a month before you can take them in otherwise they will just fizzle out.