If it's blowing out, it won't draw cold air IN. BUT... you would only want to run it a limited time once a day. When it got down to freezing here, I ran the fan anyway for about ten minutes and it cleared the room pretty well.

It does get to be a hassle, because mine is a window fan, so I have to open the window, put it in, turn it on... run it a while, then turn it off, take it out, close the window.

Usually I just have a plastic hanging and I tuck the plastic up, turn the fan on. But there's too much air leaking in when the fan is off if I don't take the fan down and close the window completely.