Chicago has America's second best public transit system, so driving is not necessary. If you must drive, the biggest obstacle is traffic. Chicago's main roads are consistently backed up during the day, especially during rush hours. Parking can also be a challenge, especially in the Loop. Many attractions have their own parking lots, but paying for a space can add up.
All things considered, driving around Chicago is actually quite easy. The city is laid out in a grid pattern, and nearly flat. If you miss a turnoff it's easy to loop back around.
In the winter, snow can make driving conditions hazardous. It doesn't faze the locals, but those without snow-driving experience will want to avoid it. Also remember to pay attention to parking rules with regards to snow plows.