Did you go to a Cincinnati Public School? I grew up in western Hamilton county (Cincinnati area) in the 50's. Regardless of the weather we walked to the main highway to catch our school bus. No matter how miserable the weather Mom did not drive us to the bus stop and I remember being really cold, hot waiting for those school buses. The only days we were inside at school was when there was snow on the ground or it was raining. I remember snuggling up to a corner of the school building for warmth on chilly, windy days. In the winter, we bundled up in layers, wool and cotton and went out to play every day after school. On snowy days we got our hats, socks and gloves wet, went in and dried them out and went out and played in the snow some more.
As an adult I ski 3-4 days a week and I especially love the snowy days when other skiers are bailing because it's too "snowy". I do dress in my "high tech" layers to stay warm on lift chairs but rarely get cold or need to go in for a warm up.
When I was teaching I thought the temp rule was silly because the kids weren't dressed by our adult standards. Many of these kids were latchkey kids who had no opportunity to go outside once they got home. They needed physical exercise every day. The excuse of no hats and gloves was lame too. Our lost and found boxes were full of hats, gloves, jackets and coats that no parent or child bothered to claim. At the end of the school year they were washed and donated to charity.
I agree that we are coddling our children too much and are encouraging the rise of obesity in our youth.
The weather in Missouri isn't all that different than Southwestern Ohio. The kids need to be outside every opportunity they can get, even if it's only for a few minutes.