That miners often worked naked or partially naked is definitely true. That children, men and women worked together in mines is also true. If it's legally allowed, then it's going to happen basically.

That there were owners who preferred children/women over men, is probably false. They will have tended to do different jobs in the mines, but I can't recall having ever read anything about a mine that preferred to not employ any male miners.

That the workers worked naked because of owner mandates is also going to be false, because those miners used to be paid according to how much they extracted, so there was no reason for the owner to have such a mandate. Instead it was the workers their own choice: some clothes hinder them in their work (heat, snagging, dust) + the job eats up clothes + they have to pay for their own clothes = they're not going to be wearing many clothes at work.