My 1/72nd scale figure collection is primarily the US Army and enemies.
Here is American Army horse cavalry for World War Two.
The horse cavalry was in use officially until near the end of World War Two.
Horse mounted troops were used in both ad hoc units and several official units in combat until the end of World War Two.
The main weapons would have been pistols and other standard weapons for dismounted use.
Of course, not all of cavalry work was exciting charges.