The German Wikipedia entry is pretty telling too.

Zugluft kann Muskelverspannungen (Muskelverhärtung) hervorrufen, insbesondere wenn der Körper stark schwitzt und nicht bedeckt ist.^[1]

Then you click the little [1] for the source and realize it's not a peer-reviewed medical paper, but rather a clickbaity article based on an interview with a single doctor, aimed at a non-specialist audience.

Als Begleiteinflussgröße kann Zugluft den Ausbruch von Infektionskrankheiten wie der Erkältung nach einer Virusinfektion begünstigen.^{[2] [3]}

Where [2] is a book that appears to be a single doctor's non-peer-reviewed treatise on the subject and [3] is another clickbaity interview with that same doctor.

Heaps of solid medical evidence. I'm convinced.