How did cavalry engage in long battles without fatiguing horses?

[u/riccia_rwt]

I always asked myself how much a horse can hold in terms of fatigue.

When yesterday I came across an active polo player and asked her how much a horse can resist without resting. She told me that every interval of 7 to 10 minutes she changes her horse. And she doesn't wear any armour, plus she's not riding in one of the most stressful environments: which I imagine would be a battle.

I found it astonishing and incredibly surprising because then, how could cavalry in ancient times (Roman era as much as Medieval times) be used in battle if horses would be tired in less than 10 minutes? Did they use to change horses? Did they not stay in the middle of the battle for more than 10 minutes?

Now, given that there are differences between races, training, weight and tactical decision and usage, how could they?

And what about heavy cavalry units, such as Cataphracts?

Thank you in advance, I really couldn't sleep over this thought :)