Horses habitually running at 60 mph over long distances is a highly implausible scenario. Here is why.
Stamina versus Speed
You are mixing up two things in your mind: stamina and speed. Living things don't work like machines. They can exert a lot of force for some time (max speed) and some force for a lot of time (stamina).
The fastest speed attained by any land animal is that of a cheetah's which runs at 60 mph. According to Guinness Book Of World Records, the speed record of a horse is: The highest race speed recorded over two furlongs is 70.76 km/h (43.97 mph) and was achieved by Winning Brew trained by Francis Vitale (United States), at the Penn National Race Course, Grantville, Pennsylvania, United States, on 14 May 2008.
I don't say that it is the maximum output possible by the biological constraints of a horse's body, but it is certainly close. Take for example the case of weight. Cheetahs have a weight range of 35-65 kg (National Geographic). On the contrary weigh between 380 and 990 kg (Horse - Wikipedia).
Which means that a horse is at least 5 times as massive as a cheetah. The speeds you mentioned in your question (60 mph) are for a sprinting cheetah. The cheetah can maintain these speeds for several hundred meters before slowing down. A horse would have much lesser stamina than that (as hinted in the world record mentioned above).
Only few horses would be able to achieve the speed of even 50 mph. And that too, would be not for more than 400 meters or so. We are talking about ace horses here, trained by the best trainers available.
So no. Even if Henry Ford had invested in faster horses, they would only be able to run at around 50 mph (the very best) for short distances (around 400 meters). No need for much protective gear I guess.
Probable Safety Gear
The most fuss you could make about safety gear for horse riders would be the same which motorcyclists use. Motorcyclists resemble horse riders in the way that they sit atop their ride and the ride is not enclosed on the sides. However motorcycles are dumb machines (as opposed to smart horses) and they are two wheeled (as opposed to four legs) and racing motorcycles run at much faster speeds than race horses. The protective gear which motorcyclists wear should easily do for horse riders too.
That would include a helmet (obvious) and limb protection (against scratches).
Also Keep In Mind
... that horses have metallic horseshoes. Which means that running on man-made roads would lead to a lot of accidents (slipping, as horses hooves would not get enough grip/friction on the roads). You would want to run your horses on dirt roads. And if you are a millionaire, you might want to build rubber tracks for providing extra friction to your prized horses.