Minnesota: Minnesota has a lot of the same advantages that Wisconsin does over Iowa, but shares a longer border. Southern Minnesota and Northern Iowa are basically the same thing, mostly dotted with small to medium sized towns. I think Minnesota would focus their attention more towards Wisconsin, with the Twin Cities being so close to Wisconsin and their general rivalry in everything. Due to this, Iowa could hold firm or push slightly north into Southern Minnesota. I have a hard time seeing a big conflict between Iowa and Minnesota breaking out.
Wisconsin: Small border to protect that is completely fortified by a good sized river. They would have trouble invading Iowa. They do have a solid population advantage, have acclimated to colder weather, and have lots of forest land to hide in. An Iowa invasion would be difficult due to those factors, plus the fact that their large population centers are spread out and a decent ways from the Iowa border so no surprise attack would be easy to accomplish. I see a border standstill here.
Illinois: The problem with Illinois in this scenario, is they would probably have an internal war before war with other states. Chicagoland vs most of the rest of the state. They could cannibalize themselves weakening their ability to fight other states. They do hold a significant population advantage, but again, that is mostly the Chicagoland area which is a good distance from the Iowa border. If they did break out into an internal war, Iowa could quickly capitalize and align with the rest of the state to combine forces to fight Chicagoland and create a standstill blockading Chicagoland in. If that didn't occur, the situation is different. Again, large disparity in population, however, the shared border is a large river that could cause issues for an invasion by either side. I see a standstill of some sort occurring here.
Missouri: Missouri is a state that shares a large border with Iowa with no natural impediments preventing an easy attack. They also have a significant population advantage. Their population is spread out making an Iowa attack tricky because too many resources focused to one side opens the other up for attack. Or Missouri could blitzkrieg fully across the border in an attempt to overwhelm Iowa. As noted by others, they also have multiple military bases within state borders along with the 'hillbilly' type. Their varied terrain is also an advance for their defenses, where Iowa is more open from a terrain standpoint. These factors would all present a significant challenge to Iowa. I do believe Missouri would initially focus their attacks on quickly overwhelming Kansas due to their shared hatred for each other, but with the advantaged Missouri holds I don't forsee the Kansas defences holding long, allowing Missouri to fairly quickly overwhelming them and then being able to focus elsewhere.
Nebraska: Nebraska is set up well to make a quick attack on Iowa, with the vast majority of their population near the Iowa border. The shared border is also fairly large, so there would be ample areas of opportunity. However, If Iowa could withstand the initial surges, most likely in the Omaha/CB area, then the rest of Nebraska is ripe for the taking. The biggest challenge would be the AF base in Omaha and if Iowa could neutralize it quickly enough before Nebraska mobilized it for offensive purposes.
South Dakota: Small shared border with them that could be relatively easy to protect plus a small population - not worried about them. Iowa could either build a strong fortification to secure the border or if getting more ambitious, make a strong push to take Sioux Falls and the rest of the state would fall fairly quickly.
Based on all these factors, Missouri is state to be most afraid of in a state vs state civil war.