As someone who raises horses and other animals, I can say with pretty high certainty that most of the horses were not allowed to "retire". Horses are expensive and time-consuming to care for, and with no practical use, most horses would have been sent not to the glue factory but (at that time) to the butcher and their non-meat parts used for fertilizer.
Was wondering about that but then came across this passage in the paper:
“ The last date on which a transient was observed within a nuclear testing window in this dataset was March 17, 1956, despite there being an additional 38 above-ground nuclear tests in the subsequent 13 months of the study period.” I would expect to see artifacts of the tests themselves continue under that hypothesis. Of course this raises a whole bunch of other questions…