Update.

On Monday we put in a formal appeal to Chop customs for an extension of stay for the horses. We are now being helped by Igor Parkhomenko, the Managing director in Ukraine for the French freight company http://www.geodiscalbersonge.com/ and he has submitted the same in Kiev.
Today Natalia (and Igor) spent most of the day trying to find out what progress has been made. Eventually Natalia got through to Chop, only to be told that they had no knowledge of the appeal and no record of the case reference number! It was only after talking to them for about an hour that they finally discovered the appeal and have now logged it into their computer system. They also told her it would take about 15 days to process, until she pointed out that in two days time the horses will be illegally in the country. She has now got the name of an official (they declined to provide me with one when I submitted the appeal) and will contact them tomorrow for progress.
All very depressing, and I was only cheered up when Igor burst out laughing when I told him the saga!  I think I need to develop a Ukrainian attitude to Soviet style bureaucratic circumlocution.