People come to work hungry, clothes getting tattered, overseer needs them working, but some women have to reenter the home to take care of basic needs Due to circumstances, women forced to work all jobs 'Gee Boris, I'd love to get my hair done up and put on my dress instead of these pants, but its -30 degrees and I have to work a 12 hour shift!' I suspect certain groups of women would forgo dresses entirely, and get real snitty when people complained about their lack of feminity. Women would go from traditional 1860's garb, to far more practical outfits. You'd see fashion changes pretty hardcore. I'd have a big scene were a woman either decides to cut her hair because of where she's working or have a woman get her hair caught in a machine to terrible results. Women are smaller, so you might have some tasks in a confined area that its hard to find a man to work in, but a woman could easily fit. In factories, its going to depend heavily but those could certainly be mixed gender. The workshops would probably be more of a combination though fewer women probably due to a generally weaker educational base. You'd see women dominating the medical field pretty quickly. In terms of assigned jobs, women don't have the same upper body strength as men so some jobs like coal mining would be male dominated but children were used as miners so certain women would do fine there. Some women would be resentful of having their traditional role taken over by machines, others would love it (both cases depending on job). Realistically things like laundry and other tasks they traditionally performed would likewise get mechanized so they could enter into the labor pool more fully. I suspect you'd see an initial phase where all women were forced out of the house to help, which would be immensely useful but then you'd start to see problems (clothes not being washed, kids not being tended) so you'd see things like cookhouses getting made so women didn't have to do that.

WW1 and WW2 saw significant participation of women in the production work force. Women were needed for production jobs rather than homemaking and traditionally they responded very well to that. There is a disaster and all hands are needed on deck to keep everyone alive. I could go on, but lets leave it as that was important and go onto the current setting. Most time saving technology was at its infancy, so washing clothes, critical if you wanted them to keep, was an all day activity. Note, back in that timeframe, keeping up a house was a full time job and very important so for the baseline functionality of the family unit.

Frostpunk takes place in an alternative 1886, so you'd have a scenario where the traditional role of women had been in the home, taking care of the children and keeping house.

Frostpunk lore