Probably all medieval monarchs wore fur garments when the weather was cold enough.
But what seems to be the normal medieval picture of monarch in civilian dress was to wear a long robe with a cloak over it, often made of richly decorated silk.
Here is a link to a medieval image of Emperor Frederick I (r. 1152-1190):
https://www.gettyimages.ch/detail/nachrichtenfoto/frederick-i-barbarossa-12th-century-holy-roman-emperor-nachrichtenfoto/463894779#/frederick-i-barbarossa-12th-century-holy-roman-emperor-13th-century-picture-id4638947791
Here is a link to a medieval image of Emperor Henry VI (r.1190-1198):
https://en.wikipedia.org/wiki/Henry_VI,_Holy_Roman_Emperor#/media/File:Codex_Manesse_Heinrich_VI._(HRR).jpg2
Here is a link to a medieval image of Emperor Frederick II (r. 1216-1250):
https://en.wikipedia.org/wiki/Frederick_II,_Holy_Roman_Emperor#/media/File:Frederick_II_and_eagle.jpg3
Here is Holy Roman Emperor Francis II (r. 1792-1806) in his coronation robes handed down from medieval emperors:
https://www.pinterest.com/pin/353603008224103162/4
Here is a medieval picture of King Richard II of England (r. 1377-1399) wearing robes and a cloak. Note that two other figures in the painting wear ermine fir collars around their necks.
https://en.wikipedia.org/wiki/Richard_II_of_England#/media/File:Wilton_diptych.jpg5
And here is a medieval painting of the same King Richard II wearing ermine fur:
https://en.wikipedia.org/wiki/Richard_II_of_England#/media/File:Richard_II_King_of_England.jpg6
A medieval painting of the coronation of King Charles VI of France (r. 1380-1422):
https://en.wikipedia.org/wiki/Charles_VI_of_France#/media/File:Couronnement_de_Charles_VI_le_Bien-Aim%C3%A9.jpg7
King Francis II of France (r.1558-1560) and Queen Mary of Scotland:
https://en.wikipedia.org/wiki/Francis_II_of_France#/media/File:Francois_Second_Mary_Stuart.jpg8
King Charles X of France (r.1824-1830):
https://en.wikipedia.org/wiki/List_of_French_monarchs#/media/File:Charles_X_Roi_de_France_et_de_Navarre.jpg9
King George VI of the United Kingdom (r.1936-1952):
https://en.wikipedia.org/wiki/George_VI#/media/File:King_George_VI.jpg10
So when and why was there a change in the formal dress of European monarchs?
Can anyone point to online discussions or articles about that change?