Both Iowa and Iowa State have hockey teams that participate in the American Collegiate Hockey Association (ACHA). Iowa State competes in Division 1, while Iowa in Division 2. Iowa is not on Iowa State's schedule this year and maybe hasn't been for many years, so I can't dispute your claim that Iowa is better. Some years you can find that Iowa State fields teams in all three divisions as well as women's teams. That surprised me as I've only heard about the D1 team.
Club hockey is a big deal for many schools, including those that have NCAA Division 1 teams. It's surprising how many teams there are.
Iowa State has been very successful over the years. As of 2018 had been to at least 14 Final Fours, 9 championship games and won at least one national championship. History is a bit hard to come by as the ACHA has only been around 34 years and it's hard to find what it was before that.
Iowa State has been playing club hockey for 57 years. Following the team suspension for the 2022-2023 academic year, the Iowa State Men’s Hockey Club has returned to the ice and has altered its organizational structure, now becoming a fully student-run organization. I don't think they have fully recovered from the suspension.
When Hilton was built in the early 1970's they had an ice floor and could push back what was once called the arena circle so boards could be put up. If you look at Hilton today, you can see how the arena could easily host hockey. Home games were played in Hilton when I waa a college student. They occasionally had open skating in Hilton for students. It was quite a blast. But after hosting home games for 12 to 14 years, hockey at Hilton came to an end. Some claimed the ice made the basketball court slick. I think Johnny Orr had a hand in bringing it to an end.