Can you wear a hat to a Catholic funeral?

It depends on your gender. Woman are allowed if not encouraged to cover their heads in a Catholic church and therefore may wear hats or veils appropriate to the occasion. This goes as well for when at the cemetery.

Men must remove their hats out of respect to God when in a church and when on hallowed ground. It is also a common sign of respect to the deceased as well as the others whose bodies are buried in the cemetery.