The bad blood saw Mr Peters in Parliament likening Tauranga-based Mr Horan to late British broadcaster and alleged child sex offender Jimmy Savile on Tuesday.
Mr Horan promised to hit back and did so during the Budget debate.
Mr Horan told Parliament he was writing to Speaker David Carter to ask him to investigate NZ First's use of "taxpayer-funded software for party political purposes such as campaigning and fundraising".
He said NZ First paid "tens of thousands of dollars out of the Leader's Budget to develop this software and has their Parliamentary staff working to run the programme for election year".
"This is a clear breach of Parliamentary Service guidelines."
Mr Horan provided documents to the media yesterday including an email which stated that "a number of fulltime parliamentary staff are engaged to run this programme".
"Peters and his staff are well aware they are blurring the lines between party political and Parliamentary business," the email stated.
Mr Horan told the Bay of Plenty Times the accusation was "something that was necessary that I was challenged to produce that I produced".
Speaking from Auckland, Mr Peters said Mr Horan's claim was "a lie" and denied the software was used for party political purposes.
"It's used to enable our expansion into sector groups, all sorts of commercial and social interest groups where we're able to spell out what our policies are and interact with them."
"It is run by someone who knows precisely what the law is as to the appropriateness of use and what you can and cannot do."
Mr Peters said Mr Horan was making allegations "that are just baseless like the one he made about a $2 million slush fund, that's a total lie as well, and the one about the horse is a lie as well."
Grant Duncan of Massey University told the Bay of Plenty Times the recent sniping was "pretty mucky and awful".
"If you're going to have freedom of speech unfortunately we are going to have to live with some yucky things," he said.
"Obviously there's some bad blood between these two men and Winston Peters clearly would like Brendan Horan out of Parliament so he can restore his proportionality in the House. The Jimmy Savile accusation was well below the belt."
Despite the accusations and name-calling Mr Duncan said the continuation of parliamentary privilege was a necessity so "genuinely serious allegations" could be made.
