I understand your pain Wheatermay. For the longest time, I just thought my horse was a dark bay
until someone on here corrected me that she is brown and I now see the error in my ways. Looking back, I can't see how I missed she was a brown, but I definitely see it now.
Like what was said above, the easiest way to spot a brown is the "cinnamon" coloured points on their muzzle, flanks, etc. The other giveaway is the sometimes drastic difference between Winter and Summer. Many browns look just like a Bay in summer and the lighter orangey points sort of blend into the rest of them, but then becomes more obvious in Winter when darker hair comes in. I've posted examples of my mare below, although I think at this point, you probably catch the drift.
Lilly a few summers ago - she has darkened significantly since then, but you can see how her lighter points kind of blend in with the rest of her and how I mistook her for Bay for the longest time. Her coat colour varies from year to year but has remained darker for the last few.
This is not a good picture because she was super fat this summer, but you can really see her lighter points on her inner legs, flanks and face.
Wintertime - lighter points really stand out. You won't see those softer points in Wintertime on a Bay like you do with a Brown.