During the US Civil War (1861-1865) Mexico was involved in its own war, the Second French Intervention (1861-1867), which occupied most of its resources, there were offerings by the Confederates to obtain Mexican help in the war in exchange for returning Mexican territories and from Lincoln to buy Baja California, ostencibly to "shield it from Confederate aggression".
But both came to naught for obvious reasons, besides this, there was constant contact between Lincoln and Juarez (Lincoln along with Ullysses Grant having been both outspoken critics of the US-Mexican War) through Juarez's wife Margarita Maza, who took residence in Washington at the outbreak of French aggression(1) and served as a sort of diplomatic jack-of-all-trades throughout the war, facilitating Union support to Mexico through the loan of money, guns, cannons, supplies and "accidentaly" leaving abandoned caches of weapons and ammunitions which the Mexican Juarist forces just "happened to find" from time to time.
May be something of a tangent, but the US Civil War almost drove the Canadian Horse to extinction, and they are still considered threatened.
The Canadian horse descends from French stock sent to Canada by Louis XIV, and they became a very widespread and popular in the northern United States as they are a pretty tough breed. However, the US never tried to set up their own stud or breeding program, continuing to import them from Canada. They made pretty good artillery horses, fitting this description from the diary of John Gibbons perfectly:
"The horse for artillery service should be from fifteen to sixteen hands high ... should stand erect on his legs, be strongly built, but free in his movements; his shoulders should be large enough to give support to the collar but not too heavy; his body full, but not too long; the sides well rounded; the limbs solid with rather strong shanks, and the feet in good condition. To these qualities he should unite, as much as possible, the qualities of the saddle horse; should trot and gallop easily, have even gaits and not be skittish."
And then the Civil War happened, and LITERALLY MILLIONS of horses died, many of them Canadian Horse, and the population collapsed. There was no formal veterinary branch of the Union Army - the US Army Veterinary Service wasn't founded until 1916 - and animal welfare was not as rigorously enforced as it should have been.
In 1849, there were approximately 150,000 Canadian horses. In 1880, they were almost extinct, and in 1913, their export was banned. Even in 1976, there were less than 400 and even today there are only a couple of thousand.
The Canadian Horse is an Official Symbol of Canada, and the Civil War combined with overenthusiastic exportation meant that it very nearly went extinct and hasn't exactly bounced back.