Is the Hubble Ultra-Deep Field image representative of the entire sky?
Short answer: both.

HUDF is representative on the type of galaxies we can find at that distance (and remember that distance also means time ago).

On the other hand, we do not really know how the galaxies are grouped beyond certain level, but we think they are grouped on so-called filaments, leaving enormous empty voids.



In this sense, HUDF's density does not represent the entire sky.

http://cosmicweb.uchicago.edu/filaments.html