I don't know if this is the 3rd Regiment's song or not, but the stage Irish song "Forty Miles a Day on Beans and Hay" or "Regular Army-0" has two verses near the end that refer to Crook's abortive campaign in Montana. Our group does it once in a while at heritage day shindigs.

The Crook verses are:

T'was out upon the Yellowstone
We had the damnedest time
We made the trip with Rosebud George
Six months without a dime
For fifteen hundred miles we went
Through hunger, mud and rain
Our backs all bare, no rations there
No chance for grass or grain

With your bunkie starvin' by your side
No rations was the rule
Sure it's eat your boots and saddles, ye brute
Save the packer and the mule
But when it came to fightin'
No soldier lad was slow
For it wasn't the packer that won you a star
In the regular army-o!

Chorus:
Oh there was Sergeant John McCafferty
And Corporal Donahue
They made us march up to the crack
In gallant company Q
Oh the drums they roll, upon my soul
For that's the way we go
Forty miles a day, on beans and hay
In the regular army-o!