They won’t need nukes. State armies won’t withstand conventional bombing. The east-west “union” army just has to control the airspace and fly the bombs in with drones or high altitude planes.
Much of the US air force would go over to the Free States and much of the aviation industry is in the south and midwest. The bigger problem for the free States is not air superiority, I think that is draw, the South/Mid Free States will have trouble getting up to speed with armor. The North does have the edgy as all tanks are now made in Ohio.