I don't think there is much difference between men and women dress during OT days. It was something like raincoat or overcoat . It evolved rapidly and quickly reached a level where a wide difference was unavoidable . Not only that , women dress became a sorce of mind corruption (sin)for men. St.Paul raised the issue because of this aspect , I believe . It is not that women barred wearing men's robe , but it is that women shall not wear dress in such a way to lure men commit sin. Who would object if a woman want to wear coat & suit , instead of jeans & t-shirt ? If St.Paul live today he would have object even women's dress of today ( tight-fittings , transparency , cuttings & exposure ,short nature etc. )Wearing modern women dress is more dangerous than wearing men dress of Bible times.