Yes, almost always.

The ancient Greeks used a Krater to mix their water and wine. Wine was a big part of Greek and Roman culture, so keeping it watered down was very important.

I can't speak for Roman culture so much, but in ancient Greece drinking undiluted, full strength wine was something of a faux pas. It meant you were a drunkard who couldn't restrain himself.

For the most part wine was diluted simply because most people drank wine instead of water throughout the day, so in order for you not to be totally hammered by 11:30 am you would have your wine watered down.