A. P. Hudson's "Folksongs of Mississippi" has:

GOING TO THE MEXICAN WAR

I'll take my knapsack on my back,
My rifle on my shoulder,
I'm going away to the Mexican war,
I'm going to be a soldier.

The streets are lined with $10 bills,
The girls are sweet as candy,
Coffee grows on white-oak trees,
And the rivers run with brandy.

Kind of like the Big Rock Candy Mountains.

Jean Ritchie's "Singing Family of the Cumberlands" has nearly identical verses as part of a play-party version of "Old King Cole."

And see this thread:

https://mudcat.org/thread.cfm?threadid=31537

In fact, most versions have "Mexican war," "Mexico," "New Orleans," or "the old Rio Grande." Joh Hartford sang a verse (learned, possibly, from a recording of W. Va. fiddler Ed Haley [1885-1951]) that said, "I'm going down to Shiloh."