While I do not think that face features that arise from Down Syndrome would be linked to the disease since there is a small chance for another person to also have Down Syndrome in the same community at the time. I have heard an article about skeletal remains of children with Down Syndrome that was buried in the same manner as other people and they were suggesting from this that they were treated no differently than other people - but can we extrapolate that fact simply from the manner of their burial?
Is there some evidence of a mystical explanation for Down Syndrome from the people in the Middle Ages? I don't want to be rude here, but would they suggest that they are possessed by demons or are "trolls" or any other mystical creature from the culture? I find those explanations for mental illnesses as demon possession interesting and how the culture shaped those explanations and how those illnesses shaped the culture.
/u/sunagainstgold and /u/itsallfolklore are featured in How were intellectually/developmentally disabled people generally treated in the West before the 20th Century?
See also the Monday Methods post about disability.