Looking further in passenger lists I found a Peter Horvath who arrived in New York on the Karlsruhe on 3 April 1901 planning to go to Lehigh Co., Pennsylvania, to meet Mihal Horvath. This looks like the Peter I'm looking for. He was Hungarian and his home town is unreadable to me. The Ellis Island website has it as 'Pieszczohoza'. Again, a town I cannot find listed in online gazetteers.
By the way, I looked for Mihal and found one Mihal Horvath arriving in New York from Hamburg on 3 April 1900 on the Belgravia. He was born in 1874 and was accompanied by Laslo Fazakas, Georg Lazar and Janos Fazakas. All four were from the same town as Peter. No luck yet finding them in census records or naturalization records.