"The Trail to Mexico" is a closely related descendant (a version in DT) as pointed out by Malcolm Douglas. Some versions are very close to "Early in the Spring," but this one is more in the western idiom.

THE TRAIL TO MEXICO

I made up my mind in the early day
To quit my crowd that was so gay,
To leave my native home for a while,
To travel west for many a mile.

'Twas in the year of '83
That A. J. Simpson hired me;
He said, "Young fellow, I want you to go
And follow my cattle into Mexico."

He gave me a horse and a pack sack too,
With an old tin can and a big bed roll.
We throwed them dogies out on the trail
And we headed them west into Mexico.

We rode the trail where the bullets flew,
Where Indians many and cowboys few.
We fought our way everywhere we'd go
As we pushed that herd into Mexico.

I wrote a letter to the girl I love,
I said, "I'm true as the stars above."
She said, "I've found me a richer love,
You can follow them cattle into Mexico."

I wrote a letter and this I said,
"You've got you a millionaire instead-
It's curse your gold and your silver too,
God pity a girl that van't prove true!

"I'll shoot my way to the western trail
Where the Indian bullets fall like hail,
I'll live my life where the dogies go
From old Fort Worth into Mexico."

The days were hot and the nights were cold,
As the dogies cried and the longhorns lowed,
'Twas a long and a lonesome go
From Abilene into Mexico.

I'll get me a girl at the end of the trail,
A cow girl's love will never fail,
You cannot buy her heart for gold
On the sun-baked prairies of Mexico.

Library Congress, Woody Guthrie Manuscripts, quoted in Fife and Fife, Cowboy and Western Songs, 1969 (1982), pp. 179-182, versions A-E with music. Text E, "Going to Leave Old Texas Now," has lyrics unrelated to the rest.
By 1883, the only human problems in this area were rustlers and a few thieves. The bullets reflect the shot and shell of older versions from UK. The western song first appeared in John A. Lomax, Cowboy Songs, 1910, with no notes.

Other versions preserve lines like "don't go where the bullets fly, curse all the gold and the silver too, married a richer life," etc.