Forgive me if I have offended anyone, I was under the presumption that the purpose of a forum is to openly discuss ideas and provide suggestions so the OP can make an informed decision. You are more than welcome to disagree with me, rebut my suggestions, or provide alternatives. That’s how we as a society learn and grow.
While I am certainly no expert, I can tell you that without a heat source, insulation will not make a barn warm. Insulation will retain heat from the horses, but two horses in a 48’x36’ barn is not much of a heat source. The large, thick-walled (stone) barns in Europe that you referenced were far more densely stocked because animals were typically kept in narrow stanchions, not roomy 12’x12’ stalls. BTW, the insulative value of 12 inches of stone is about the same as 1 inch of wood, R-1. I cannot see any way to insulate those 12x12 sliding doors on each end of the barn; thus they will always allow the cold Minnesota temperature to pass through freely and are not much better than an open door, except that they do block the wind, which is a huge boon. Do you disagree that a properly-ventilated barn will allow the heat to dissipate through the roof cupolas during the winter?
You mention that filling a wall cavity with loose straw is “an unbelievable fire hazard”. The autoignition temperature of straw is 170°F. Are you suggesting that the metal walls get that hot in the Minnesota Sun? Maybe they do, in which case, you would be correct. If not, what’s the ignition source? Keep in mind that the OP will be storing baled hay in her barn, which if it is not properly cured is probably the #1 cause of barn fires; another major cause being electrical problems (overloaded circuits, chewed wires, etc.). Just things to keep in mind since we are discussing hazards.
Moving on, Simkie has decided on the Foamboard. The other choice, Reflectix, is worthless as insulation – it’s value relies upon reflecting radiant heat and you need at least 1.5 inches of space on either side for that to work. I have it installed under the purlins of the metal roof of my home, which I personally built, and let me tell you that it reflects some intense heat back into the sky. Ouch that’s HOT! Bad choice on my part. It does keep out the heat, but the intense heat is causing my paint to prematurely fade. Live and learn. The Foamboard should be clad in wood to keep the horses from eating it, I would imagine. The autoignition temperature is fairly high, around 700°F. That’s good because I was concerned about the hot metal siding causing it to burn. The Foamboard is R-5 per inch, which s decent. Not sure how thick you were planning on using, but I would fill the entire wall cavity for two reasons: (1) more insulation is always better, imo and (2) ease of installation. Incidentally, rigid insulation can be cut very nicely on a table saw, as I can attest from experience, although you can also use a circular saw. No matter how much insulation you install, I’m not sure you can keep the air temperature inside the barn more than 20°F above the outside temperature without supplemental heat. We use an oil filled space heater in our cathouse and sometimes the cats actually sleep on top of it at night.
You’ve got a real nice place there, Simkie. Best of luck.