The equestrian events of the 1956 Summer Olympics in Melbourne, Australia, were held in Sweden.

The Olympics are almost always held in a single country, in a tradition that goes back to the International Olympics Committee’s first games in 1896. But on a couple of occasions the Summer Olympics have been held in more than one country – and in 1956, they were held in both the Northern and Southern Hemisphere.
The host city was Melbourne, Australia. It was in and around Melbourne that most of the sports took place: gymnastics, sailing, wrestling, basketball, cycling, etc. There was just one problem: the equestrian events. At the time Australia had some very strict quarantine laws, and they refused to relax those laws for the Olympics. All competitors’ horses would have to be isolated for six months.
There was a lot of back and forth between the IOC, the Australian government, and the Melbourne hosts before a compromise was reached: the equestrian events would be held six months before the Australian events, in Stockholm, Sweden… almost as far away from Melbourne as it is possible to get. In Stockholm they had a parade (on horseback), lit the Olympic torch (also on horseback), and ran all of the equestrian events for the Australian games. It was apparently a huge success.
The Melbourne games are also the first time all the athletes mingled together in the closing ceremony. An anonymous letter sent by John Ian Wing, a 17-year-old Melbourne carpenter, pointed out that everyone marching separately seemed against the spirit of the games. So they changed the closing ceremony and it has been that way ever since.