Ok I'm new to this site and to the whole genealogy thing so I'm not even sure if i'm doing this right. But i'm pretty sure this info is accurate.

the 1910 Census states that Joseph, Mary, Willie J and "Steafman" ( Stephen ) Horvath came to US in 1904.

I could not find the actual Passenger list from the 1904 immigration, but I did find later documents stating they immigrated in 1904 and naturalized in 1917.

Then Again in 1922, a The New York passenger from 9 Oct list states that

Joseph
Mary
Stephen
Joseph Jr.
William J
Lajos
Peter
( all Horvath )

came to the U.S. again

Joseph states that his nearest relative is his son, Vince Horvath, in Papa, Hungary.