Are there still "prairie dog refineries"?
Any collection of 'hooch stills' that were soldered (?) together would probably have been uneconomical almost as soon as they were built, because welding together a series of serviceable fractional distillation towers is not that technologically advanced and much more efficient.  However, there are certainly a number of relatively small refineries.

For instance, about the largest refinery in the U.S. (for comparison) is Exxon's in Baytown, TX that has a capacity of 560,000 barrels per day.  

A couple of the smallest ones are the 5000 bbl/day refinery in Wyoming (Silver Eagle, in Evanston) and the 2000 bbl/day Foreland Refinery in Ely, NV.  The latter (if run all day) is equivalent to around 1.5 barrels a minute.  

Also (to respond to a comment) there are still some refineries that don't do catalytic cracking (probably just straight distillation of the petroleum into fractions, which is viable for small refiners because they can save on expensive (and often proprietary) cracking units and are small enough that they can sell all the fractions that they produce.  The recently closed Flint Hill refinery in Alaska used another approach, reinjecting unused fractions back into the TransAlaska pipeline.)

For a list of refineries, the EIA is always a good place to look (pdf warning).

A wiki on refineries is "A Barrel Full" which has detailed information on individual refineries.