In her 1998 post linked above, Alice recalls children singing "Walking on the Green Grass, Green Grass", The children then added the lines "We're going to get married".

IMO, that song is a combination of "Walkin etc" and a variant form of "Dukes A Riding".

For comparison, see this song that I collected in 1997 from an African American woman's memories of her childhood in the 1950s Pittsburgh, Pennsylvania:

Directions: The girls are in one group and the boys are in another.
In the 1st part of this song, the girls sing and skip four steps for each phrase toward the boys and the boys sing while walking four steps for each phrase toward the girls. In the 2nd part, after the girls shout "Are you coming?" and the boys shout "No!, the girls try to catch the boy whose name was selected and the boys run away, protecting that boy from being caught by the girls.

[First Part]
Girls:        We're riding here to get married
        Married, Married
        Riding here to get married.
        Ah Rhythm A Diddee
       A Diddee High Oh

Boys:        Who you gonna marry?
        Marry, Marry
        Who you gonna marry?
        Ah Rhythm A Diddee
       A Diddee High Oh

Girls:        We're gonna marry Johnny *
        Johnny, Johnny
        We're gonna marry Johnny
        Johnny, Johnny
        Ah Rhythm A Diddee
       A Diddee High Oh

Boys:        How ya gonna get him?
        Get Him, Get Him
        How ya gonna get him
        Ah Rhythm A Diddee
       A Diddee High Oh

Girls:        We'll break the doors and windows
        Windows, Windows
        We'll break the doors and windows
        Ah Rhythm A Diddee
       A Diddee High Oh

Boys:        You'll get all dirty and greasy
        Greasy, Greasy
        You'll get all dirty and greasy
        Ah Rhythm A Diddee
       A Diddee High Oh

Girls:        We're not as greasy and you are
        You are, You are
        We're not as greasy as you are
        You'll get all dirty and greasy
        Ah Rhythm A Diddee
       A Diddee High Oh

Second Part:
Girls:        Are you coming? {Spoken loudly}

Boys        NO!(Yelled)

{Girls chase the boys, particularly trying to catch the selected boy, but actually trying to catch any boy.

* Use the name of the boy selected to "marry".

-snip-

IMO, this rhyme probably comes from the rhyme "Here Comes A Young Man Courtin" that is included in Thomas W. Talley's "Negro Folk Rhymes" {Port Washington, N.Y, Kennikat Press, 1968, pp. 85-86.; originally published 1922.} And I believe that that rhyme is based on the British game song "Here Comes Three Dukes A'Ridin."

In Talley's version, after the lines "Here Comes A Young Man Courtin", the "brown skin ladies" say "Won't you have one of us, sir?" and the men reply "You is too black and rusty, rusty rusty". The ladies then respond "We hain't no blacker than you sir" etc. Talley's version then demonstrates the color prejudice of those times by havin the "yaller girls all gay" ask the men "Pray, won't you have one of us, sir?" The men respond "You is too ragged an' dirty" etc." The "yaller girls" then say "You shore is got the big head, bighead, bighead bighead, you sure has got the bighead and you needn't come this way." The yaller girls" continue by telling the men "We's good enough for you, sir". The men respond to this by askin for "the fairest one that I can see to come and walk this way". The ending refrain for these verses is "Tidlum Tidelum Day"

I should however note that in their "Singing Game" book the Opies describe an advancing/retreating performance style for at least one version of "Walkin etc." That performance style is similar to that described in the first part of the "We're Riding Here To Get Married". I believe that it was also the performance style of "Three Dukes A Riding" and I'm wondering if "Soldier Boy" is/was performed in the same manner.