Ward is a three-time Olympic medalist having claimed gold medals in Beijing and Athens and a silver in Rio. He will be making his fifth Olympic appearance at the Tokyo Games, which begin on July 23.
Kraut also won gold in Beijing, while Farrington will be hoping to add to his silver from Rio.
Springsteen, ranked 27th in the world, will ride 12-year-old Belgian Warmblood stallion Don Juan van de Donkhoeve in Tokyo.
“Some horses, you get on immediately and you click right away, and others it can take a little bit longer and be a bit of a struggle.
“But I think you have to be patient and it has to be a mutual give and take between the horse.”
She added: “I think the key to getting the best out of your horse is just managing their schedule, making a good program in advance. You can pick shows that you think they’ll peak at.”
The jumping team qualifying event and final at the Tokyo Olympics take place on August 6 and August 7.
Aly Vance contributed to reporting.