One of the persistent myths of alternate history fans is that Lord Wellington was asked by the British government to invade the United States from the Gulf Coast in order to defeat the upstart Americans in the War of 1812. [Example here.]
Whether or not there ever was a formal request made by the PM to Wellington, Duke Wellington supposedly declined, without grace or patience. Thus, it is a speculation without content. It is so counter-factual, in fact, that there is not a single fact out of the period and location, to fuel such useless speculation.
Nevertheless the speculations continue apace, taking it as a given that this general, who was so good at his work that he defeated Napoleón himself in a battle -- a battle, let me haste to say, that didn't take place until after the first abdication of Napoleón, which concluded the Congress of Vienna, in which the surviving powers were wrangling over the division of the spoils of Bonaparte's empire, and Wellington was a primary player.* With some level-headed dissenters, war gamers tend to believe that Wellington have quickly cut a swathe through the former colonies and returned them to British rule. This fuels ever more extreme counter-factual speculation as how would change the course of world history.
There is not a single fact upon which to build speculations. In contrast, however,, there are ample facts that strongly suggest that Wellington showing up on the Gulf coast would have been as much a debacle as it turned out for British army general, Edward Pakenham, and British naval commander, Admiral Alexander Cocherane -- and very likely in the same way.
First he'd have had to defeat Andrew Jackson, who knew his territory, as he proved over and over, from the Floridas and the Gulf, all the way up the Natchez Trace and the Mississippi Corridor to Nashville, the water and land routes both, in this vast Louisiana Purchase territory. Whenever Jackson encountered the Brits in the Floridas and the Gulf, he'd defeated them (and hung some, even though it was illegal). He'd been doing this long before the Battle of New Orleans.
This wasn't Wellington's geography, or the geography of any regular army, as the British learned in the War of Independence. They occupied all the cities, but it did them no good (except to give contemporary Americans a silly idea of their own competence and exceptional capacity for success purely through the actions of single individuals, conveniently forgetting the essential roles of France in Spain in the ultimate outcome).
There were no places other than New Orleans to re-supply a Wellington army, and it was very far away from the hinterlands. There were no plantations to plunder yet, but those around New Orleans and Natchez. The land was covered in dense forest, swamps, bridgeless rivers and bayous. The American forces were skilled at living rough and at brigandage. They'd have been at least as fierce a guerrilla third front as Wellington had encountered in Spain, except these would be working against him.
As intensely as Wellington had put himself through a military education he'd surely read the history of the War of American Independence. As much time as he'd
spent in Spain, he'd surely have at recall the large role Spain's General Bernardo Galvez played in the Gulf Mississippi Valley in defeating the British back then and there, and how easy it was for him to do so, since the British military were not good on that ground. Moreover, now, in the present of the War of 1812, which in any case, as mentioned, was now over, Spain was Britain's ally.
So, yes, there are many facts that show Wellington, if, indeed he was formally asked to fight in North America, made the right decision to stay on this side of the Atlantic, while there is nary a single one to say he'd have met anything but disaster, whether by water, cavalry or infantry. His artillery would have been as prone to incapacity by corrosion and mud as anyone else's, especially without roads along which to push them. The horses would die from starvation, and the men as well.
* Which was a fortunate circumstances for Britain and the rest of Europe, since Wellington was already on the ground in central Europe, where war was resuming, not sitting around uselessly in the Americas, where that war was over. The Treaty of Ghent had been signed December 24, 1814.
Wellington, where he was, was perfectly positioned to take immediate charge of the British forces and confer with the generals of the other powers' armies during Napoleón's 100 Days: 20 March to 8 July 1815.