Red barns started in Europe hundreds of years ago. The barns would be sealed with linseed oil to protect them from the elements and to prevent the wood from rotting. The oil has a naturally tan color.
At some point, farmers started adding rust to the paint. Rust kills mold and moss that would otherwise destroy the wood. Eventually, by the 1800s, there was no real need for the paint to be red-colored but the tradition of having red barns has remained until today.