That tiny coop shouldn't house more than 2 hens for very long. I would consider it a very temporary arrangement.
I would also brace and secure a 2x6 (long side vertical) over the center of the "run" area of the pre-fab coop to form a small pitch. Then secure a tarp over that section to try to keep it dry-ish over the winter.
You want to shoot for a coop with 3.5-4 sq ft of floor space, 12" of linear roost space and as close to 1 sq ft of permanent ventilation as you can manage per bird as well as 1 nest box per 4-5 birds. The run should offer another 15 sq ft of space per bird and don't leave it bare. They like to scratch around in organic matter, perch and preen at various times of the day and dust bathe. They will dig their own sites but the run must be kept dry not only for hygiene reasons and to keep parasite loads down but also so they have good dust bathing sites. Always put clutter in the run in the form of stumps, old wood chairs or stools, pallets, whatever you have that would be fun for chickens to jump up on.
The hens on the ground behind the stump are bathing:
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I would also put a solid roof on the run and make everything walk-in style as it makes life ever so much easier and enjoyable. I converted an old shed on my property into my coop and it was absolutely the best thing I ever did for ease in their care.
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