I don't know why toy soldiers have long been associated with Christmas and apparently the internet doesn't know either. The closest guess anyone comes to is their link to "The Nutcracker" and it's "March of Toy Soldiers".
At any rate, Christmas is what I thought of when I saw these plastic blow mold soldiers.
The cannon can (or used to be) fired by slamming your fist down on the back of it, or squeezing the sides of it, which launched the yellow plastic "cannonball". I would guess the object was to line up the soldiers and knock them down by shooting them with their own cannon. Seems unsporting.