Bitter Cold here in Wisconsin the next few days......

[Soon2BChixMom]

Sounds like you have a good set up, I assume your run is also covered?
My run is wide open, just a small space(4x7) that is pretty sheltered.
Most days I let them decide whether to go out or not, some go out and some stay inside. Some will walk in the snow, others will not.
Days like today when it's snowing gangbusters and 8F, I left the pop door closed after checking on them. Will probably open it later when I shovel part of the run clear.

To answer your question, most will seek shelter. I don't think the cold ground bothers them much, not like us out there barefoot. Birds have a special adaptation that controls blood flow to the feet to protect them.

The set up is not a great one since it is a prefab, but it is off of the ground and so they use the space under the coop right now for their outdoor time. This is the area wrapped in plastic and it keeps pretty dry. - I have a run extension that has a tarp covering it, but that has snow and they don't seem to like the snow, so they stay only under the coop and in the coop. When it's not blowing snow, I add fresh shavings to the extension area so that they will venture out there, but if it's blowing there is no sense in doing it.
I'm looking into building a better coop in the spring. I can see now why a coop needs more space - especially in inclement weather.

 

[path.otto]

In summer I isolate and give electrolyte/vitamin mix(Sav-A-Chik), had to hand feed all day once.
Never had one fail it in winter...not sure what I would do, maybe same thing

I wouldn't worry about this at all except I have 2 pullets that are molting and the BO is looking a little pathetic although no where near the photo you posted of a hard molt. The coop is insulated, they have protection from prevailing winds in the run, they have fresh unfrozen water, a little scratch before they go to bed, food available in coop and in run and on these really cold mornings I give them about a tablespoon of warm oatmeal each just for a kick start.

It's a good thing I like cold weather because I spend a lot of time checking on them!

 

[hillbillyreefer]

This is the first winter that we're not adding any supplemental heat, and I am really worrying about our chickens. They seem fine, but it's been really cold, and no relief in sight. So do your hens prefer the shelves w/bedding to roost on, rather than just regular roosting bars? That is a good idea, I bet it's warmer than just sitting on a 2 x 4! We put LOTS of hay in their pen where they hang out all day, which they like to hunker down in, but nothing like that where they roost. I'm just wondering if they would like it if we put boards w/hay on their roosting perches, or if they prefer actually gripping a bar when they sleep?

They seem divided on what they prefer, there is room for all the birds on the shelves and there is also ample space for them on the bars. I feel when it’s bitterly cold more use the shelves than the roost bars, but I couldn’t prove that empirically.

 

[MarcieR]

We added an outside "redneck" shelter for our hens. We had an old truck cap with the back hatch door missing. We put it up on straw bales with the opening facing east. The other windows are intact. We placed their dust bath under this and they spend a lot of time in their shelter during this cold weather. Love upcycling! BTW, my husband is the softy, he keeps worrying about adding heat. I just keep saying "they will be fine"!

 

[path.otto]

@hillbillyreefer

They seem divided on what they prefer, there is room for all the birds on the shelves and there is also ample space for them on the bars. I feel when it’s bitterly cold more use the shelves than the roost bars, but I couldn’t prove that empirically.

@hillbillyreefer I had to laugh when I read your "couldn't prove that empirically". I made the mistake of musing "I wonder how long it takes a freshly laid egg to freeze at today's temperature" around my science-oriented husband. He has spent the last 15 minutes suggesting how I could set up an experiment to figure that out.