No wild boars at the time of the Mexican War. Don't know ho they got into your song. Only the little javelina (peccary) of the southwest border area (Mex.jabalina, or little boar, from Sp. jabali, or wild boar).
Are there wild boars now? Yes. They were brought to game ranches in the USA and Canada, and the meat appears on the menus of fancy restaurants (even in fancy groceries here now). But, like the active animals that they are, some have escaped and are becoming a problem. They are free also on the Big Island of Hawai'i where they were brought as a game animal.

Mexican War. Started as an argument over the border, but President Polk and the expansionists turned it into an opportunity to gain the southwest- New Mexico, Arizona, California, and, as they were part of these Mexican lands, parts of Colorado, Kansas, etc. etc.
Without going into the history books, this is the story of the Mormon Battalion from the summary in Cheney. "Polk and the national leaders, knowing that the Mormons were on the way to California or Oregon (names by which the western part of the United States was known) decided to make use of them to win the country. Five hundred men were called from the Mormon camps at Mount Pigsah and Council Bluffs [Iowa]. The Mormons responded...." "The march of the Mormon Battalion from Iowa to the Mexican border and thence to the sea was said to have been unparalleled in recent history in the misery it produced, though, considering the hardships of the handcart pioneers, ...an exaggeration." Levi Hancock, a folk artist, was called by Brigham Young to be spiritual advisor to the group. Hancock said "Without a guide who had traveled them, we have ventured into table lands, where water was not found for several marched..." "And General Kearney, when he heard details of the march, said..."*Bonaparte crossed the Alps, but these men have crossed a continent."
The march also had later consequences because it showed that a route to California without high mountain passes existed close to the (now) Mexican border; eventually the Southern Pacific railroad was built there.
Hancock verse:

Ere the Battalion started out
Upon that most important route,
'Twas thus predicted by the tongue
Of Apostle Brigham Young,
"If to your God and country true,
You'll have no fighting there to do."
Was General Kearney satisfied?
Yes, more- for he with martial pride
Said, "O'er the Alps Napoleon went,
But these men crossed a continent."

Brigham Young was correct, no battles were fought, only with the "wild bulls."