Parker also says he's eaten a selection of centipedes, crickets, spiders and scorpions.
Horn defeated England's Gary Corcoran with an 11th-round stoppage last month in Brisbane in his first world title defence.
The 25-year-old admitted he has to ask his mum before taking his heavyweight belt out of the house.
The rising Kiwi heavyweight scored the most dominant win of his career so far in just 67 seconds.
The NZ heavyweight fighter takes on US boxer Fred Latham in Cleveland next month.
Mick Hennessy said "stop acting like amateurs and get on with the fight, you've got your money."
Today's press conference turned into a WWE spectacle with both fighters throwing down threats.
Former DUCO boss Dean Lonergan has been at the centre of organising the fight, but tomorrow it'll all be up to his fighter in the centre of the ring.
Parker was unhappy with background issues leading up to his fight with Razvan Cojanu.