Edit: A few people are wondering why the Thoroughbred and Mustang are saddled while the Tennessee Walker isn't. This was done on purpose so as not to add any extra points of speed on the TW. I was aiming to test what the difference was between the slowest horse available against the fastest horse for curiosities sake.
Disclaimer - All testing was done in story mode. Unfortunately, horses in online are speed capped in free roam!
Rockstar hasn't released any patch notes in regards to horse speed adjustments at the time of making this video so we can only assume speed is more or less the same for online and story mode.