We know it exists. This particular census was called the "Josephine" census because it was the census ordered by Emperor Joseph II of Austria - Hungary to count men for military service  We know that some rolls of it are at the National Archives of Hungary. Some are also at Family History Archives because the Genealogical Society of Utah filmed it in 1970.
The 1857 Hungarian census (Népszámlálás) was the forerunner of the 1869 Hungarian census. It has two pages with nine columns. It listed the full names of each household member with their birth date or their age. There was a column for religion and occupation similar to the 1869 census as well as their marital status and birthplace.
This census is particularly valuable for genealogical research as it includes person's name & surname, exact birthdate for men between 14 and 20 (while others were asked only for the year of their birth), religion, occupation, marital status, place of residence, presence/absence of the person during the data collection and the information about person's livestock. A question about person's nationality wasn't included. 
The Genealogical Society of Utah filmed the counties of Csanád , Zala , Esztergom, Tolna and a few scattered towns in Zemplin and other various locations. Every reference I could find to it hints that there are more counties but not filmed by LDS. So where are they ? Are they filmed and stored in archives in Hungary or in Slovakia or even Romania ?
For a listing of the Family History Film numbers, Family Search listed them here, with a breakdown of the villages filmed: All FHL Holdings of the 1857 census
I can accept that not all census returns are filmed but what I would like to discover is a complete library catalog of all the census returns that are preserved and stored in archives. The sad fact is, by law, they had to be destroyed after the next census was taken. But in 1970, the Genealogical Society filmed quite a bunch of them that were somehow stored away. So they all of them were not destroyed.
It is reported that there were two copies and each locality was suppose to comply but many did not destroy them. There are still random accounts of county archives that might have the 1857 census. I did an inventory hoping to glean some 1857 censuses in Abauj- Torna . Still hunting but if anyone want to dig further, you can consult this pdf called the ' Census and census-like material preserved in the archives of Hungary, Slovakia and Transylvania (Romania), 18-19th centuries ' by Péter Őri & Levente Pakot . (http://www.demogr.mpg.de/papers/working/wp-2011-020.pdf) 2) Max-Planck-Institut für demograﬁ sche Forschung Max Planck Institute for Demographic Research Konrad-Zuse-Strasse 1 · D-18057 Rostock · GERMANY