Short answers, pulled from the story.
The first evidence of horses in warfare dates from Eurasia between 4000 and 3000 BC. Archaeologists have found remains of horse-mounted nomads in the steppes of what is now Ukraine, Hungary, and Romania during this period.
A major breakthrough came with the horse collar invented in China during the 5th century AD. This innovation allowed horses to pull greater weights than previous ox yokes or breast collars could manage.
Paired stirrups first appeared in China about 322 AD during the Jin dynasty. Following this invention, nomadic groups such as the Mongols adopted the technology and gained decisive military advantages.
Heavy cavalry was believed to have been developed by Ancient Persians though others argue for Sarmatians. By the time of Darius ruling from 558 to 486 BC, Persian tactics required completely armored horses and riders.
Final British cavalry charge occurred the 21st of March 1942 when Burma Frontier Force encountered Japanese infantry central Burma. Only American cavalry unit during WWII was 26th Cavalry challenging Japanese invaders Luzon holding off armored infantry regiments Philippines invasion repelling tank unit Binalonan successfully holding ground Allied armies retreat Bataan.