The 15th century was not all wars, death, disease & destruction: there was plenty of time for music and dance. We know that Richard III enjoyed musical entertainment and ‘pageants’.
One chronicler who disliked Richard III left a comment about the Christmas festivities in 1484:
it should not be left unsaid that during this Christmas feast too much attention was paid to singing and dancing and to vain exchanges of clothing between Queen Anne and Lady Elizabeth, eldest daughter of the dead king, who were alike in complexion and figure.
The Crowland Chronicle Continuations 1459-1486, ed. N. Pronay and J. Cox (Richard III & Yorkist History Trust, 1986), p. 175.
Dancing was most often performed in circles or chains with linked hands. Some of these dances were called carols and were accompanied by songs: the steps changed at the change between the verse and the chorus. We have since adopted this word for our Christmas songs.
The image of dancers on the left comes from a book that was made in Bruges for Edward IV.
More complicated dances would be performed at court. The image below shows a famous occasion when Charles VI of France and five of his noblemen dressed up as mythical creatures called wodewoses to perform a wild dance at a wedding feast. Unfortunately their costumes caught fire and King Charles was saved by the 15 year old Duchess of Berry who used her skirts to smother the flames.
Morris dancers have been performing since the 15th century.
In England circle dances were popular.
More elegant forms of dance developed in Italy and France (Provence and Burgundy) and were adopted by the English Court during the 15th century such as the basse dance for couples.