Executioners worked very differently depending on which country they were from and even which region ( or county / duchy / city, ...Etc ). That is why executioners did not obey to the same rules and laws depending on the location and time period. I'll write a bit about executioners in France, based on Frédéric Armand's Executioners in France ( original title Les bourreaux en France ).

The profession of executioner was one you would not really like to do. Not so much because of the nature of job that the place it gives you in society. Professional executioners ( in the surroundings of Paris and some other locations, professionals were those who had received a letter of provision, a royal decree according you an office ). In other places, until around the XVth century executioners were not always professionals but gravediggers for example or even criminals which were offered a lighter sentence or freedom after putting other criminals to death. While almost no one rose a voice against death penalty, a deep disdain and/or fear was held against executioners. Merchants refused to sell them their goods, they could not send their children to school, the Church even had to authorize marriage between executioners families ( who often had a very high rate of consanguinity hence the involvement of the Church ) because nobody would allow a daughter to marry an executioner's son so they married between themselves. If you know about French traditions, you may know that in a lot of families you can't put your bread in the wrong way on a table and this comes from the fact that bakers put a cross on the belly of the bread they reserved to the executioner so they they did not mix the breads. Laws had to be created to ease the executioner's lives such as the droit de havage or havée ( the right to take ) which allowed them to have food reserved for them.

As such, " dynasties " of executioners were born ( some very famous like the Sanson ). Their families were all related and this all the way until the 20th century and the abolition of death penalty. Executioners lived on the side of society. As such, it is perfectly fair to imagine why executioners were heavily romanticized in poetry, fantasy or Hollywood movies but they did not have hoods or masks. Instead their distinctive cloth was a some sort of cloak or coat with the executioner's sign, a sword and a coat. You can see in various representations of executions that do not wear masks like here or there .

However, this does not mean that nowhere or at some point in the world were hoods and masks not used. In France for example, before Saint-Louis reformed the judicial and penal systems it would not surprise me if an executioner wore this kind of clothes or anything else more or less " strange ". Also, Jacque-Augustin de Thou, a French writer and judge wrote in his Universal History that the executioner of Mary Stuart ( I Know this is not really the middle-ages but ... ) had a mask. However from what I read de Thou's work on the matter has to be taken with a big grain of salt.

Someone else could write about other places. But executioners in the Middle Ages ( and even after ) are not the easiest topic. People avoided interactions with them as much as they could and their lives and roles were heavily romanticized by writers and/or clerics and this is not something new.