It's possible you're thinking of a few things:
* Dorsal stripe: Some horse breeds, like Appaloosas, can have a stripe of darker pigmentation running down their back, but this is not always red. The color can range from black to brown to a very dark red. This is part of their unique coat pattern.
* Sunburn: A red line down the back could simply be a sunburn.
* Muscle definition: In some horses, particularly athletic breeds like Quarter Horses and Thoroughbreds, you can see a line of muscle definition down the back, especially after exercise. This isn't actually a red line, but the way the light reflects off the muscles can give that impression.
If you can provide more details about the horse you're thinking of, like its breed, color, and what the line looks like, I might be able to give you a more specific answer.