You can always double up the plastic, you can even toss some card board in between the plastic and the coop for insulation.
This is the plastic I mentioned, this is a smaller roll so it’s cheaper. May be worth looking into when you build the new coop come spring. I’m sure your ladies will be ok, you’d be surprised what a chicken go go thru. They are amazingly hardy animals, and all around amazing
Frost King P1025/6W Polyethylene... https://www.amazon.com/dp/B0040ZC5AO?ref=ppx_pop_mob_ap_share
Try using this as a tarp and posts to support it, will keep the rain out and will help a bit with rain.
Those snow globes are about $799. Ouch!
I'm curious. Why do you say 6mil plastic sheeting (i can use clear, so it doesnt absorb as much sun&heat) is better than a heavy duty tarp?