This is helpful information, particularly with regard to classifications and the differences between a borrower with a work visa and a true foreign national.
True foreign nationals are defined as those buyers or borrowers who primarily live overseas and earn qualifying income in their country of origin. It is very unusual for a foreign national to have a Social Security number, but some do. It is certainly not required to have social security number nor an ITIN, but practiced and active investors will eventually obtain an ITIN.
Work Visa borrowers may get 95% to 97% financing and Foreign Nationals are generally eligible for financing at 55% to 75% LTV, both second homes and rental property. For foreign nationals, this is usually a conventional loan but may not be a conforming mortgage. There is a fair amount of both vacation homes and rental units (investment property) being financed.
$104 billion in U.S. real estate was bought last year by foreign nationals, and if I remember correctly, 55% was bought all cash, so the 45% remaining, by extension, must have had some kind of financing.
Paperwork requirements differ from lender to lender and the lenders in this space include banks, insurance companies, hedge funds, etc. It is NOT a cakewalk to get financing, however.