The horse was sired by famous racehorse Zabeel and has itself claimed more than $20,000 in prizemoney in the past year.
On Tuesday, Mr Horan used parliamentary privilege to accuse Mr Peters of misusing his $2.5 million leader's budget.
Mr Peters, NZ First's racing spokesman and a former Racing Minister, strongly rejected both claims.
"This stupid allegation comes from a thoroughly discredited nag that crashed into the first hurdle," he said.
He believed there was no requirement to declare ownership in a horse, let alone a 10 per cent stake in a syndicate lease of a horse.
The lease, which was bought in a charity auction in 2008, has now expired.
MPs must declare all property, directorships, gifts, shares and other interests in the register each year.
Registrar Sir Maarten Wevers said he had not received complaints on the issue, and it was up to each MP to decide whether or not something fell within the terms of the register.
He said the ownership of racehorses by MPs had been raised with his office previously.
Sir Maarten said racehorses that were held by syndicates needed to be declared, but he did not know the full details of the ownership structure of Bellazeel.
"I would think it would certainly be ... a business entity undertaking ... something for a pecuniary profit. That's what you race a horse for, I presume."
Mr Horan and National MP Chris Tremain have previously disclosed part-ownership of a racehorse in the register.
Mr Peters declared a company directorship, two properties, two blocks of land, a superannuation scheme and overseas travel in the latest returns, which were published last week.