The logistics have not been easy, because the Hong Kong races only occur on Wednesdays and at weekends and there are other, rather more serious matters of protocol which must take priority. But Mr Cook is a frustrated race-goer. When he came to Hong Kong for the handover to Chinese rule on 1 July, the horse-racing season had finished. On a visit in May 1996, the season was on but Mr Cook had to get back to London to attend to urgent parliamentary business. So he is leaving little to chance for this third official visit.
The Foreign Secretary will therefore be in Hong Kong on Wednesday, 21 January to start his official meetings in the former colony. And that evening he will be sitting in one of the luxury boxes at the newly refurbished Happy Valley racecourse. There is little flexibility with the date, because Mr Cook's trip to China and Hong Kong has to take place in the week of 19 January in order not to clash with the previous week's visit to Peking of Margaret Beckett, President of the Board of Trade .
Any further delay, and he will run into the following week's Chinese New Year holiday, when China effectively shuts down. He also has to fit in with the travel plans of his counterpart, Qian Qichen, who is due back from a trip to Africa just before Mr Cook's China visit.
Planning meetings are taking place to try to find a way of accommodating the demands of horse racing and Sino-British relations.
At first it was suggested by the British that the problem could be solved if Mr Cook arrived first in Guangzhou (Canton), moving from there to Hong Kong, and then to Peking for a day of meetings on Thursday, 22 January.
To Chinese eyes, this would be a big break with established diplomatic protocol, which demands that a visiting foreign secretary should make Peking the first stop on the mainland.
Nevertheless, a request was made to the Chinese for this schedule.
Before the Chinese replied, the logistical problems of organising this itinerary began to worry UK officials.
It would have meant Mr Cook leaving the Happy Valley race track just before the last race on 21 January. He would then have been whisked to the airport and flown by a government VC-10 to Peking, arriving early on Thursday, where Chinese protocol officials would have had to turn out in the middle of the night at the airport to meet him.
Nevertheless, this was still the plan at the beginning of this week, but wiser counsel seems to have prevailed. The night at the races is still safe but the Guangzhou stop of the visit has been dropped, despite the original notion that it was useful for Mr Cook to see somewhere in mainland China other than Peking. The British side hopes Mr Qian will be available slightly earlier that week, so Mr Cook will arrive first in Peking and fly to Hong Kong by Wednesday, and back to London. He will not get the chance to see a bit more of China - but will get to Hong Kong in time for the races.
One obvious benefit of the revised timetable is that Mr Cook will be able - if he wishes - to make use of normal scheduled flights, rather then needing his own plane for a late-night Hong Kong-Peking flight.
Although the planning of the visit has been complicated by the lure of the turf, Mr Cook has serious business to transact. The main purpose of the visit is to build on the warming relations between London and Peking since the Hong Kong handover. He will also lay the ground for the planned Tony Blair trip later this year. Mr Blair met President Jiang Zemin in Hong Kong the night of the handover, with much banter from the Chinese side about the youth of the new British Prime Minister.
Mr Cook's love of horse-racing might also make for some friendly exchanges.
Chinese officials love going to the races in Hong Kong. Larry Yung, the son of the Chinese vice-president Rong Yiren, is a senior steward of what used to be called the Royal Hong Kong Jockey Club - now simply known as the Hong Kong Jockey Club.