How far are you willing to go?
You can get a lot of mileage out of replacing the horse biology with something more effective. Other commenters have mentioned you could make the horse eat on the run or make the lungs bigger, but consider more extreme alternatives.
Cycling Respiratory System
Pigeons breathe more efficiently by having multi chambered lungs that cycle air constantly through multiple chambers instead of pulling in and then emptying, which would allow your horse to have better airflow.
Myogolbin storage changes like deep swimming creatures would also allow your horse to store more oxygen internally at one time, it might be simpler than remaking the lungs and heart while also insuring that it can function at full capacity for longer, possibly much longer.
More or better Creatine would allow your horse to store more ATP inside each cell before needing to switch to a lower powered mode. Either just make your horse produce more Creatine naturally or feed it something like "Di-acetyl Creatine Ethyl Ester" in the feed.
It turns out Mitochondria actually float around the blood and move from cell to cell, so if you work out a more resilient form that has a more efficient energy cycle, you can just inject them into the horse with a syringe and they'll naturally propagate.
These points are fairly low lying fruit that will naturally give you a stronger and faster horse without any change to its food or other lifestyle. But you could probably go much further...
That pesky biology
If you think about it, a lot of your neo-horse is dedicated to carrying around that pesky stomach and its associated waste control organs. But you wouldn't need them if you were able to substitute the horse's energy needs with an external source.
You still need a way to get proteins and micro-nutrients into the horse, but one thing you can do is inject Ketones into the horse through some kind of internal (and refillable) vein attachment (cyber fuel tank basically). Ketones aren't as efficient as normal oxygen-glucose processes, but they are fairly self contained and mostly generate only Co2 and water as a byproduct.
Some kind of refrigeration system in the saddle would be useful and would probably make a huge difference to your horse.
Certain types of bacteria and some synthetic proteins are capable of doing the proton pump process purely through electrical power. This means that in theory you could generate ATP inside your cells without any input or output products, purely through electrical power. If you're injecting new mitochondria like in the step outlined above, you could modify them with this process and some way to accept electrical power wirelessly, possibly from the saddle or some other implant. If it works, your horse is now at least partially battery powered. You don't even need 100% coverage, as any amount of coverage removes that amount of load from the lungs/digestion/kidneys etc of the horse' biology.
Of course, at the end of the day it's still a horse, which means it needs to run around on four toothpick legs and will fall apart if it sees its own shadow.
But new materials like graphene fiber are far more resilient than regular muscles and tendons. If you had some way to make the horse generate these proteins internally it would be both faster and more resilient. Something that might be possible if your horse has more energy to burn on internal maintenance.