When it gets real cold things can change alot. Foxes hunt first light and right before dark alot more and day time more. They even lay out in the sun alot when it is cold. But 32° is not cold to them. I think when it gets real bad out they go down holes were it is warmer at night.
It all depends on what you are thinking cold is. Coyotes your guess is as good as mine. But they shoot alot in real cold wheather in the day time. What they do at night is any ones guess. But I have seen and killed them is some real cold weather at night.
I would hunt after lunch in the winter if I were you and you know were some are hanging out.