To pull a door to - means to shut it but probably not completely - it may be touching the door frame but not securely closed. For example, if I want to go out to my car to get something, I might pull my front door to, meaning that it isn't properly shut but is lightly 'jammed' into the frame - that way it looks closed at a quick look but I don't need to take my key to unlock it again as I can just push it open. Saves messing about with my keys when I'm only going to be a few seconds but it's more secure (and warmer) than just leaving the door open.
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