This is a partial answer as I don't have full evidence to support it, but I suspect that the Chinese may have employed mounted infantry in wartime as late as the 1970s.
From page 15 of China's War Against Vietnam, 1979: A Military Analysis:
Advancing rapidly at the outset, the Chinese forces soon met with
difficulties. The rugged terrain of the mountainous border area was
substantially unfavorable to the movement of division-sized forces,
trucks, and other motor vehicles. The Chinese, lacking modern
logistics equipment and being refrained from using air transportation,
were forced to rely on old trucks, horses, donkeys, and laborers for
I will claim that it's plausible the Chinese used mounted infantry in combat during this conflict, simply because it's a matter of record that they had the units available in their armed forces for use (with soldiers were trained to fire weapons from the saddle, not just use them for mobility in the fashion of dragoons), the difficult terrain could've made their use advantageous for the same reasons as in say Afghanistan, and as donkeys and horses were already being used as beasts of burden for logistics purposes, they obviously had the "meta-logistics" required to feed and care for animals set up for the war.
If I can find any solid references to support the claim, I will append this answer; it's a bit difficult as while there were nearly 60,000 soldiers KIA during about a month of fighting, which certainly fits my definition of a "major war", it's a bit of a "forgotten conflict" and there don't seem to be a huge number of primary sources to draw from (in the English language, at least.)