Is frostbite avoidable without electric heating? Should I add heat to my coop?

[Ponypoor]

Here is a picture of my OSB ceiling - to me that doesn't really look like mold, just normal OSB texture. I am no expert when it comes to this and have never dealt with mold, so it could be, I just don't know. And in person, the spots look much lighter - like a reddish brown.
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Here is another one of mine:
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To compare, this image below is a google image of an OSB board, and it looks very similar to mine. Mine is a bit darker, but maybe that is just shadows/lighting? Who knows... I will keep an eye on it.
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Looks fine.

But I would paint it in the summer to prevent any issues down the road.

A nice light paint will also help keep it nice and bright in there when it’s gloomy

 

[SourRoses]

Here is a picture of my OSB ceiling - to me that doesn't really look like mold, just normal OSB texture.

I had cropped and posted a picture of the affected part of your ceiling. Along with a description of exactly what I was looking at.

We know what particle board looks like. Honestly, most people seal it as part of the construction process due to the hygroscopic properties.
If you really don't want to, that's your choice.

 

[StinkyAcres]

One sure way to lower humidity in the coop below the exterior percentage, is horse pine pellets as bedding.
They are super dry and help the whole coop climate. In FL we get rain so often my coops would mold without them.

@ChickenShepherd_6116 I actually see some mold on the particle board in one of your photos.

I personally would not choose deep litter in any walled space for the humidity issue.

Particle board makes it harder to see mold, but see how, in this picture, along the bottom third the board you have a mix of light and darker wood... But in the upper two thirds you see black spotting. That's the mold.

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I would paint the interior if it was me, since mold started will only get worse over time. Killz makes a paint with antifungal properties that will kill it as you paint.

I don't see any mold in this photo either, at least nothing major.

 

[SourRoses]

I don't see any mold in this photo either, at least nothing major.

I understand where you're coming from, really. It is nothing major, for now. I pointed out the beginning of it. But it most likely will get worse at OPs humidity levels.

My parents owned a construction company so I've seen the affects on particle board from minor mistakes in construction. My mother always referred to it with a frown because she had to help fix the problems. It's both universally hated in construction and widely used due to the cost factor.
I double checked with my mother to see what she thought and she said (of unsealed particle board) "If it's not molded yet, it's going to."
However, take this with a grain of salt, there's tons of trustworthy resources online and there are real life professionals that can advise. I also shared the option of testing to verify the presence of mold.
We often share opinions here to help each other save money. Building a coop is expensive and it should be protected.
And... Something I did not want to overemphasize due to concerns of fear mongering... But it should be said clearly. Black mold is a severe hazard to human health. Just ask some trusted internet resources "how much black mold is dangerous?".
People have died. But we had some folks here suggesting to scrub at it. No mention of PPE. The desire to underplay the issue is a little mind boggling to me, but maybe that's because I can hear the muttering of my carpenter grandfather echoing in my ears.
I'll bow out now, with sincere good wishes.