Here I am.
Swords are not bayonets, of course, and vice versa. The ability of the cavalry for mounted melee rather implies that they have the weapons to enable them to prevail. Cavalry had carbines and pistols, all single-shot weapons, so when it got up close and personal, the saber was the weapon of choice. It is an implied weapon, and I believe it would be redundant to also have it specially noted in the pdt. Frankly, the subject never came up, that I can recall.
JF