“Today, some historians suggest that the real trouble for women came with the cultural changes of the Renaissance in the 15th and 16th centuries..”
More likely the Reformation and the dissolving of monasteries played a role because the women within those had a large degree of independence both financial and personal.
Another myth is that people of that era were always dirty. It is true they hygiene was limited compared to now but they knew to keep their hands and faces clean. Bathing was not unknown but having access to clean water for bathing could be difficult.
In addition to that, how eager would you be to wash up in cold water in the dead of winter, without central heating? Doing more than washing up the hands and face in winter sounds like an awful time. Heating enough water to bathe requires a lot of fuel and work.