I've been working on cleaning up the picture. I went over the whole thing with a barely damp cloth to get off any dust and dirt. There was a little area of mold on the back of the frame. I treated that with alcohol then lemon oiled the whole frame. It's looking pretty spectacular now.
My cousin gave me a picture of the horse that was what my grandfather copied for the inlay. I think it's a lithograph but maybe it's a print like we know today. I don't know when they started doing them. Someone in the family had put it in a crummy frame to protect it. That picture included the name of the horse, Lou Dillon. By enlarging the barely visible signature on the painting and enhancing it with GIMP, I was able to see the artist was George Ford Morris, who painted mostly horses.
Lou Dillon was a Standardbred trotting horse that broke the 2-minute mile with a time of 1:58-1/2 seconds in 1903 and gained world fame. Here's the
Wikipedia page on her.
The original he worked from:
As soon as I get the history of its making attached to the back of the inlaid picture (not permanently affixed to the picture itself but in a plastic slip cover tied to the frame brackets) I will get it hung on the wall to enjoy.
On a side note, my grandfather was a building contractor who worked full time on the Winchester home until Mrs Winchester died.