“I took part in this fancy dress competition with the aim of providing light-hearted entertainment for those in attendance,” Rose wrote in a Facebook post, which was later deleted.
“If my costume/s offended anyone I am truly sorry as this was never my intention. I would like to apologise to anyone that I offended.”
Rose won team eventing silver at the 2008 and 2020 Olympics and bronze in 2016.
He said he hoped the incident would not affect his Olympic preparation, while expressing a desire for the situation to be resolved quickly.
“With a bit of luck this will all be a bit of a laugh in a few days and we can all move on,” he told the Sydney Morning Herald.
“I wore a costume which you could see at a theme park or a beach. Potentially no one has done it on (a) horse, but there you go.
“I think I am a good person and I do a lot for the sport, and for people in different situations. I don’t feel like I have done anything particularly bad.
“In hindsight, I should have re-thought what I did but, at the time, I thought it was just a bit of fun.”
Equestrian Australia chief executive Darren Gocher said a complaint was made about how Rose was dressed and that there were children at the event.
“Whether it is one (complaint) or 1000, we have an obligation to review it,” he said.
“He hasn’t been sanctioned, he hasn’t been suspended. He has been stood down from competition while we review and we have committed to getting the review done this week.”
Many members of the equestrian community were not impressed with Rose being stood down, with some changing their Facebook profile pictures to Borat in a show of solidarity.