For once, the MFA’s search engine trumps the Met’s (hat tip to Sharon for pointing out painted versions).
Brace-back Windsor side chairs, Providence, 1780-1810. MFA Boston, 1976.776
Providence, thank you very much, green over black paint. Here’s another chair, clearly green. (This is very interesting, as the ones in my museum are not painted. Clearly, there’s wide range and variation in chair finishes. Now to think about temporal and geographic distribution of those finishes…)
High fan-back Windsor armchair, Boston area. MFA Boston, 64.86
My first concern was location. All I can tell you right now about the one I found is that is seems to be from New England: much more looking to do to narrow this down to a state. (Most of my furniture time is spent looking at shells, feet, and splats, but I like the Windsor style better, so this will be fun.)
Once I figure out where the chair came from–if I can–then I can decide whether or not to strip it. The easiest thing is to clean it and then repaint it in proper colors (like green over black, happily documented to Providence).
If the preponderance of examples I find like this are not painted then I will have to look at the condition of the wood (hmm…might not be so great) and see what I think. Somewhere I even think I’ve seen a furniture check cover for a Windsor chair in a painting…always more to hunt for.
Kitty Calash 
This is a timely post. Thank you. I’ve been stressing offer a poor chair that was sadly covered in white, exterior house paint. It helps to know someone at a curatorial level also stresses over paint.
Oh, curatorial is all about stressing things…poor house painted chair! This one was painted with some kind of latex, I think, so even to paint it will require some kind of treatment. (sanding, or additives to milk paint).
I’m always amazed by people do to old things.
I can tell you /nothing/ wants to stick to this white paint and it is a nightmare to remover with all the curves on this chair. I hope you find an easier solution to your find.