I'm in Northern California so our winters are mid 30's-40's. We had a foal born November 8th this year, and it was colder than normal dipping down to right at freezing a few nights. We kept him locked up at night and double blanketed. Daytime removed one blanket in the early a.m., and unblanketed during the day - rain or shine. He had a very thick coat and within a week was out with the rest of the mares/foals. I did notice he's put on more weight than the spring/summer foals. He's doing wonderfully even with all the rain we've been getting. My horses tend to view shelters as ideal places to pee/poop, but not get out of the elements.
Last February, we had a mare foal out on our property in a rain storm, fortunately it wasn't freezing cold (mid 50's). But he was a really fuzzy, chunky foal at birth. He did fine without ever being blanketed more than a day or two. He probably didn't need it, but I did it anyway.
You really need to consider your area as everyone's setup is different and also what you're comfortable with. How much rain do you get? Wind? Snow? All of that needs to be considered.
I do remember being in your position eleven years ago. I bought three Minis and found out when they were delivered one was pregnant. So I stressed and worried and bought everything I thought I'd need. The mare foaled on her own (she's the one that had the last foal in February too - super sneaky mare), and is an excellent dam. If I a horse could laugh she would have while I was running around like a chicken with my head cut off doing all the things we need to for a new foal.
On a side note, I personally don't believe air tight barns are good for horses. Many develop respiratory infections from the lack of fresh air circulation. Straw, hay and bedding are dusty, add to that mold and urine regardless how clean you keep it. In winter the build up can happen and make your horses sick. My .02.
Unless you have an ill horse or one that is clipped (for showing) or are in extreme temperature conditions, Minis tend to do quite well with the elements. They're very hairy insulated and have access to good hay (internal heating), they keep quite warm. What mine do not like is rain that is blowing sideways. It doesn't drain off well and they get wet to the skin.