The name is a reference to Boaty McBoatface, the leading choice in a public poll to name a British research vessel.
The horse was named by trainer Bjorn Baker's team at Sydney's Warwick Farm racecourse.
Mr Baker's racing manager Jack Bruce told the BBC they held high hopes for Horsey McHorseface.
"We bought him from a ready-to-run sale in New Zealand where he put in a very good breeze (gallop)," Mr Bruce said.
Horsey McHorseface was bought for NZ$65,000 ($45,000, Â£32,000) in November last year and shipped to Australia.
He is now being prepared for racing at Mr Baker's stables.
Meanwhile Boaty McBoatface remains the frontrunner in the UK's National Environmental Research Council's (NERC) non-binding poll to name a Â£200m polar research ship.
The silly name has garnered global support but it is not clear if the NERC is prepared to honour the poll result.
Horsey McHorseface is not the first homage to Boaty McBoatface - on 22 March a UK railway worker renamed the Portsmouth to Waterloo train service Trainy McTrainface.
A two-year-old gelding destined to race in Australia has been saddled with the name Horsey McHorseface.