I'm 99.9% certain we will never see HHN at Epic Universe.
The first issue is venues -- where do you put ten haunted houses? USF has the soundstages, parade buildings, Sprung tents, etc. which make an event that revolves around temporary walkthrough attractions practical. Will the new park have equivalent spaces waiting to serve such a purpose? Probably not.
The next issue is capacity. This is the main reason why the event left IOA. The most horrific thing at HHN is the crowds, and the park needs to be able to accommodate them. With Epic Universe's layout that requires people to enter & exit every land in the same place, to and from a shared hub area, this could be a serious issue for crowd flow. We also don't know how many people the park comfortably holds yet.
And then there's the cooperation of the IP holders. Will they even allow the event to take place in their sections of the park? We already know Fantastic Beasts is a no-go. They aren't allowed to do anything HHN-related in Wizarding World, besides having it open as normal. Will Nintendo allow it? Probably not. So despite having a permanent land based around horror, you also have an entire half of the park that likely can't even be used.
What I could see them doing is some sort of smaller scale Halloween celebration in the Monsters land, sort of like how Seuss Landing has Grinchmas, but nothing approaching the scale of HHN.