FYI, there are set taxi fares from ORD to the suburbs. O’Hare to Evanston - $32, Midway to Evanston - $55. Some additional baggage fees I’m sure.
Others have indicated the snow belt across I-94 and I-80/90 very well. I drive this frequently and have had plans disrupted more than once. The roads can be fine, then suddenly there’s a white out with zero visibility. Much truck traffic which can also make conditions even more nerve wracking. I’ve also crept along at 15 MPH seeing numerous cars in ditches. Other trips, absolutely no problems what-so-ever. It really isn’t highly plan-able from weeks or months out. Having said that, if I needed to get to Ann Arbor sometime in the next couple months, I would plan on driving. As others have said, you are best to know all the options and be ready to switch plans.
I personally would not choose Midway over ORD if going to Evanston, but the previous poster is correct that ORD schedules are often disrupted. If it was me, I would decide based on the airline cost and flight times, noting additional potential taxi cost and distance from Midway to Evanston.
Do post this in the Music Forum. There are probably families who have done exactly these visits for auditions. You may get more specific info, suggestions and experiences.