Ahhhhh what a difference good photos make! I am envious of your coop and run setup, very nice job! I love how you arranged their spaces, everything is protected from rain/snow/ice, plenty of ventilation (love the addition of louvered vents between spaces), nicely sized and placed roosts, just...
I don't think it's necessary to cover the fence part with plastic, since that's just their run - but it wouldn't hurt. It's the coop I'm concerned about and that big window. Cover the window with plastic, but leave a gap across the top, maybe 4 inches wide or so.
Oh, and dirt is fine in the run; I thought your photo was inside the coop where it needs to have bedding, chips, leaf matter, straw, something covering the floor to absorb droppings.
She appears to have enough feathering to withstand some cold temps, as long as she's not in a draft. Does she have friends that she cuddles up with on the roost? That helps.
Chickens can withstand very cold temperatures, even below zero-F, and do fine. BUT they have to be DRY, protected from DRAFTS, and have access to fresh WATER. I see gaps between those boards on the walls. Is the outside covered with plastic? You do not want any air blowing in between those...