I let Ben out because he wanted it. When Mom and I got back from McD's with what was going to be breakfast, but turned into lunch because the menu changed before our eyes, I stepped out back to see if he changed his mind about being out because of the temperature.
One of my childhood cats would ask to go out, and if there was snow, she'd just hiss at whoever opened the door before going out to pee/patrol her territory before heading back in.
Ben goes out because he started life outside. He likes being an indoor/outdoor cat now, but likes outside more. And will pee on something if we ignore him asking to go out.
He asked to be let out again. (I guess in hopes that it magically became warm enough to go out.) He did not go out. Probably part being hit in the face with cold air and part out of Mary's original kittens being right there.