This has been covered, and the consensus is that Vito pulled some strings and had Tom fly on some kind of government or military plane.
In the saga and I think in the book also, Tom comes back to report to Vito what he found out, and then they make the plan and send Luca out there. In the movie it looks like the horse died the next morning.
"Io sono stanco, sono imbigliato, and I wan't everyone here to know, there ain't gonna be no trouble from me..Don Corleone..Cicc' a port!"
"I stood in the courtroom like a fool."
"I am Constanza: Lord of the idiots."
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