There is a noticeable difference in your response rate to advertising for an open unit in the winter vs. the summer. When it is an intra-city move, I have found that my first responders are people who NEED to move and often times aren't the kind of renter's I am looking for.
Having said that, in a city the size of Chicago, people are moving at all times of the year but you should plan for a longer vacancy if you are seeking a renter in November -Jan. Just price that into your offer or look at properties with existing tenants/leases. Because the slow season is typically slower for sellers too and they may be motivated to get it sold before winter as well.
I go out of my way to avoid vacancies in November and December. But if you are purchasing, just manipulate the closing date so you aren't holding a vacant property during these times.
If you need to do work on the property anyway, you can try to get it done during the slow rent months and be ready to rent in January-February when things are moving again.
It also depends on your target renter(s) given the quality/location of the property you are seeking. Professionals move in and out of Chicago at all times of the year for work