You’ve found a frost hollow. Under calm conditions you can get cold air drainage off surrounding hills into the valleys. This valley, being surrounded by hills, will act as a basin and collect the cold air. With nowhere to drain to further, it will just sit there. Frost hollows can sometimes be 10+C colder than the surrounding hills, and also sometimes you will see a layer of stratus on top of the cold air layer blanketing the valley.
In this case it can also be made worse by the presence of the snow on the ground, which will sharpen the radiation inversion overnight and help trap the air, but also insulate the ground from the sun and prevent heating, keeping it cold.