International travel isn't a modern invention. And our ancestors were not monkeys. …
I was looking at the book on Henry the Navigator on Gutenburg's servers a while back. (Project Gutenburg) I only got as far as the Introduction before I got angry at modern science.
Since then I have had time to think. We tend to think the ancients didn't know how to navigate because they tended to hug the coastline.
But since the majority of sea travel was Mediteranean, hugging the coast wasn't much of an option. But beside the fact that the Greeks and Romans didn't have that far to go, the fact they used pottery barrels possibly held another reason for doing so. Pottery containers are rat proof. On a long voyage hungry rats can get into wood that is why ocean voyagers used oak, a very difficult wood to chew through.
But not impossible.
Putting stuff like pickled cabbage in wood was bound to lead to problems. But you can easily make sauerkraut in a galzed urn or amphora. The Romans used pottery cylinders called tuns.
They generally held 2 tons of wine hence the term ton. Tons of tuns.
Anyway the point is that had they reason to travel to the Americas, they could have done so without fear from rats or scurvy.
But what would have been the point. The Roman world held vast tracts of unexplored land in Europe and Africa. Travel much further south than Egypt seems to have been unrewarding. Even conquering Britain seems to have been a last minute idea. Apparently they couldn't be bothered with Ireland or Scotland. It was just too far from the profitable SE plains?
They didn't seem to do much outside of Portsmouth, York and London.
No place else to dump horses I don't doubt.