Kind of.
Miami picked the ibis because when a hurricane comes around, it's the last animal to take shelter and the first to reappear once the hurricane leaves. So their mascot is based off of symbolism/legend associated with a hurricane.
ISU picked the Cardinal because they realized having an anthropomorphic tornado would be pretty silly (though admittedly, if done right, could be cool). So they went to the school colors and chose to go with a Cardinal. Could have been worse. At least you guys didn't go the Stanford route and end up being associated with a horrendous mascot like the Stanford Tree...
Not quite.
Prior to 1895 the Iowa Agricultural College (later to be renamed Iowa State) was known as the Cardinals. On Sep 29, 1895 (a heavier than normal tornado year), they went to Chicago to play Northwestern in football, and were huge underdogs. Needless to say, IAC smacked around Northwestern to the tune of 36-0. The headline in the Chicago Tribune stated that IAC "Struck Like a Cyclone". The name stuck.
Fast forward to 1954, when Iowa State College was looking for ways to "increase school spirit", and an onfield mascot was decided upon. As you said, a tornado would have been difficult to do. Now, unlike what you implied, ISC didn't pull the cardinal mascot out of their arse, they did some research and learned that the cardinal was the original mascot of Iowa State. At that time they thought about doing away with the "Cyclones" moniker for the "Cardinals" name. However, they decided against that and retained the "Cyclones" nickname with the Cardinal mascot named Cy.