Will keeping the pop door open create a draft in winter?

Hi everyone, We don't have horrible winters here in the high desert. Lows may get into the 20s but usually stay in the 30s, we may get a day or two of light snow. I have a small coop (4 x 4 x 4) which houses 4 hens and we are approaching our first winter. There are small holes at the top of the coop for ventilation and an 18" square window slightly above roost height that I have now blocked off with Styrofoam, which they can't get to. I don't think that's enough ventilation so was wondering if leaving the floor level door to the run open would be ok draft-wise. I clean their coop every day so there is only a night's worth of poop to give off moisture and ammonia. I also have a layer of sweet PDZ down, mixed with the 3 inches of wood shavings that are the bedding. The one time it got cold last week, I closed the door to the run and when I opened it up in the morning, it was pretty stinky in there. What do you think? Thanks for all your sage advice. You got me through a wicked hot summer, I'm hoping my girls won't suffer the winter because of me being such a newbie.

As long as no drafts are blowing on your girls I think it's a good idea to keep it open.

I don't have a door between my coop and run, it's always open. I like the air flow and the hens always have a choice to be in or out . Unless the door is right in the line of a wind area and blowing right on the roost, I'd say keep it open.

There is a solid wall that covers that end of the run so I'm hoping a draft coming in from the low door won't be a problem. Thanks much.