I learned the Rolf Harris version as a child. The words go like this.

Two little boys had two little toys
Each had a wooden horse
Gayly they played each summer day
Warriors both of course.
One little chap had a mishap
Broke off his horses head
Wept for his toy and cried with joy
when his young playmate said.

Do you think I would leave you crying
When theres room on my horse for two
Climb up here Jack we'll soon be flying
I can go just as fast with two
When we grow up we'll both be soldiers
And our horses will not be toys
And I wonder if we'll remember
When we were two little boys

Long years passed, war came so fast
Bravely they marched away
Cannon roared loud and in the mad crowd
Wounded and dying lay
Up goes a shout a horse dashes out
Out from the ranks so blue
Galloped away to where Joe lay
Then came a voice he knew

Did you think I would leave you dying
When theres room on my horse for two
Climb up here Joe we'll soon be flying
I can go just as fast with two
Do you see Joe Im all a tremble
Perhaps its the battle noise
But I think its that I remember
When we were two little boys.

Thanks for the memory Yvonne M.