I've been in old farmhouses in Europe where this is common (also a heavy curtain near the exterior door to keep the heat in). I don't think it looks weird, although I would keep it open when anyone was over.

I have an ancient house, and there are doors to most of the rooms, but there were no clothes presses, since it was built when armoires were common. I have drapes to all the closets we have built in, and also a drape to a small bedroom downstairs. I put a drape to it since it was remodeled as a bedroom for a wheelchair bound person and a lot less cumbersome to access than a door. It looks fine.

These curtains were called portieres and they mounted on rods that are similar to shower curtain rods, set in the jamb of the doorway. (usually with rings)

palimpsest: thanks for the name of the curtains! I couldn't find any images on line when I looked up "doorway curtain" but when I looked up "portieres" I see lots of images !

Mmm, Now I wonder if I should match the curtain in the stairwell doorway to the curtains on the window in the room, also maybe I should make curtains for a wider doorway in the same room, because it gets very cold in the adjacent room in the winter. Mmmm..

scryn, your post brought back lots of memories of when I was younger and every penny was precious! The house I live in is the first time we ever had any modern heating (the heat came from a furnace in the hallway). There were lots of times I had no money to heat even this small house I have. I put a curtain between the bedrooms and the kitchen/living rooms. The LR/kitchen was left cold (or hot in summer) so I heated just the back part of the house. I can still remember scurrying in and out of that ice cold kitchen to cook meals! Even though there is a door to close off the L/R now - I still don't heat or cool it most of the time. Oh, by btw, back then my L/R furniture was gold crushed velvet, so naturally I put up a gold curtain when I closed those rooms off. lol I don't know where you live, but my sister lives in maryland and her heating bills are enormous. Good luck.