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.