One of the two big ifs of American Histor

I don't think the horse would have made a big difference. After all the horse that survived in the Americas, at the time of the arrival of the first immigrants through Bering, it was not the modern horse we know but a related species of the size of a dog.

However, I believe I can answer your curiosity that can be resumed in this:

Why the Americas was invaded by foreign peoples while Asia, Africa, India and the Middle East weren't?

There are several reasons for it, let's analize them:

(1) East Asia couldn't be invaded at all, particularly China, because the simple reason they were more technologically advanced than Europeans at the end of the 15th century! Actually, the dissaster of Spain in Japan shows it.
(2) East Asian countries that were invaded finally, where never repopulated. Why? Simple answer: distance and huge local population. It has been calculated than in phillipines, for instance, only 2% of the people has some Spanish ancestry, comparing with most of the people in Latin America that have at least some drops. Phillipines it was too far away for immigrants to come.
(3) The Middle east couldn't be invaded in mass; actually, Turkey it was invading Europe at the time.
(4) Africa couldn't be invaded either. North Africa is a hard place to invade and not quite inviting for settling. Subsaharan Africa, on the other hand, it was a place plenty of diseasses. The average survival rate of Europeans on equatorial Africa before the 20th century it was quite low. That's why the continent remained mainly unexplorer up to the Victorian age. Only Southern Africa was mild and healthy enough for Europeans to come and they did.

So, the only places remaining are the Artic, Polynesia, Australia and the Americas.

(1) The Artic was never settled by Europeans, really, with the exception of Norses. Even today, most people that live in the Artic are Inuits, because no other people can stand such extreme cold temperatures for long.
(2) Polynesia, although was invaded, it is a set of tinny islands, not very suitable for massive settling.

What remains? Australia and the Americas.

Both had something in common in the past: low density populations in most of theirs territories.Between both, they represent between both almost half the surface of the planet, and in practical term it was empty.
How many people were there at contact? We know that Mexico at the beginning of the 19th century has only 8 million people, and Chile 800.000 people. And that after centuries of importing immigrants to those regions, besides the known fact that mixed European-Amerindian hybrids were usually very fertile, so it is not wild to adventure the population at those times was larger than at contact times.

So, how many people lived in the Americas then? Perhaps 12 millions like some estimations say. Only in two regions you could find population densities over the million: Mexico and Peru.

Now, if all that is correct, the Americas just lacked the manpower enough to resist by force the invasion of Europeans and others that arrived in wave after waves. Only high tech could stop that, but seeing the tortilla wall between U.S. and Mexico today, it is easy to see that when people want to invade, just do it.
Europe at those times was the most fertile continent in the world, and exported large excedent of populations all over the globe.

That explain it, isn't?

Pinguin