Question
how cold should it be to stop watering the plant?

Answer
It is not just the temperature that slows the growth of trees--it is the amount of light and the hours of daylight as it relates to temperature. When the hardwood trees drop their leaves then the trees have stopped or greatly slowed the transpiration of water through the leaves. There is no need to supply any additional water to the trees after this time. In fact Arborvitae after the first couple of years need little additional water except during dry periods. The rainfall should be enough for them to grow well. I would mulch around them with not more than 3 inches deep of organic mulch not piled up on the trunk. This will help hold moisture around the roots during dry spell.