I think it is fair to say that in general skirts do not go at all well with socks. Skirts look fine with nylons or bare feet, but with socks the look is not good. A young woman in her twenties might be able to get away with wearing a pair of brightly coloured socks with a skirt, creating a slightly preppy or schoolgirlish look, but on an older woman this would look disastrous.
My ex-girlfriend pointed this out to me one time. She had removed her shoes at the door when wearing a long, pencil skirt and later complained that her stocking feet were cold on the kitchen floor. She asked if she could put her shoes back on. I suggested she put on the socks she had brought for with her (she had a change of clothes for when we went walking later). She did so, but said she felt very silly. She looked cute, but had looked far more elegant before she put the socks on. After this, she started bringing slippers when she visited me.
On the other hand I once invited over a girl with her husband for Sunday lunch. She was dressed very smartly and wearing a skirt with pantyhose. After she removed her shoes at the door I offered to lend her some socks in case her feet got cold. However, she had planned ahead and had brought a bright red pair of socks with her. She was obviously happy to make socks work with her formal wear.
I have a friend whose sole objection to the shoes-off rule was the worry that she might be asked to remove her boots when wearing athletic socks underneath with a skirt. Obviously, that would not need to happen if she was visiting an home where she expected shoes-off at the door. She could plan on wearing trousers or just nylons under her boots.
What if a lady with socks, boots and skirt visited a home and was asked to take her shoes-off unexpectedly? My own view is that it is okay to ask for shoes at the door without prior warning if needs be. If somebody makes an unannounced visit, the host is not likely to be dressed up, so she need not feel too self-conscious. If she is very bothered, she could always take the socks off quickly at the door.