In Germany and Austria, especially back in the 18th century, birthdays were not celebrated so much as "Name Days," the feast of the child's patron Saint. Mozart most likely would have been given a greater celebration on October 31, the feast of Saint Wolfgang even though he was traditionally given the first name of the Saint on whose feast he was born, Saint John Chrysostom.
Here is a brief video showing the apartment where Mozart was born. If you have been fortunate enough to have seen this in real life, I would love to hear about it! Please leave a comment below!