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No they were all male in the early days but you are right. They went sans clothing.

I am not sure women were allowed to watch the contests.

Of course, they had public baths then too so nudity was not a big thing.

A cursory quick search seems to say that married women were not, but maidens possibly were.

It would be much better for women to practice like this. It's a shame that the first editions in ancient Greece were only men. Segregation was very strong at the time.