RUNNING IN A WINTER WONDERLANDDD

You don't need to do anything special to winterize your shoes. You can buy commercial products designed to give you traction on ice, but as long as you are running on paved surfaces (where you can see evidence of salt), you should be fine. Snow on top of ice will give you traction, so what you want to need to watch out for are areas where the snow has been removed, but the ice hasn't been melted. When in doubt, tread very lightly or walk. If you are having problems slipping and sliding, you can pick up some very small metal screws and screw them into your shoes. As far as routes go, http://www.usatf.org/routes/. They have a separate database for tracks, if you're looking for one of those.

No reason to spend any money for cleats, really. Just make your own with an old/cheap pair of shoes. http://www.skyrunner.com/screwshoe.htm I personally run outside in the winter and just plow through the snow (it never gets super deep here though) and wear homemade spikes when my running trail becomes super icy.

What I've found is sidewalks near, or leading to schools, are usually the best tended. Similarly, retail areas have contracted snow removal and are cleaned up pretty quickly too. Sidewalks that are meant to be cleared by homeowners or apartment owners are the worst. The hardest thing for me is to plot a long route with uniform surface/snow removal. Bare pavement is fine for regular shoes but horrible for Yaktrax; hard-pack snow is fine for Yaktrax but horrible for regular shoes. My expensive running shoes hold up just fine in the salty muck, but they do not look pretty. A dark color like black or navy might hide the winter grime.

Chicago winter outdoor runner here! I do not recommend cleats/YakTax because you will more often than not be running on cleared pavement. I tried the screwshoes one year and I absolutely hated running on clear pavement with them so I now just use regular shoes. I run in the early morning, so it's still dark out, and that makes it hard to see the ice, so I guess I'm just in the "be careful" camp. klarck's suggestions of running by schools and retail places is a good one, and usually what I follow. For some reason the exception to this is gas stations. They're the worst. I don't run on the lakefront path but my understanding is that it actually is kept pretty darn clear in the winter, and if you can get to it pretty easy I would definitely try it out. The wind will likely be rougher out there, though. I definitely have to schedule my running around the weather - I'm getting my run in today before we get this supposed 6 inches of snow/ice and won't run again until people have a chance to work on sidewalks. I luckily have a drop-in track I can head to when it's really bad out, so that might also be something to look for. Are you working or a student? Your work or school might have something to look into.

I lived in Hyde Park for five years. My room-mate was pretty happy with the loop around Promontory Point, because it's kept clear and the surface is asphalt and if you're into running before dawn the sunrise is gorgeous. This other guy I knew ran along the Lakefront Path, but he ran from the point to Navy Pier and back, so maybe that says more about him than about the quality of the path. A bunch of people just did random streets near the main campus---Ellis/59th/University/55th for example. I think the university has special plows in addition to what the city runs. Speaking from personal experience biking, yes, the path is windier than areas deeper inland. Nobody I knew used any kind of traction device. The Navy Pier guy did mention that if he was going to do anything involving sharp changes of direction (e.g., ladder drills, suicides, etc.) he'd walk that stretch slowly first to check for ice.

I also love to running outside when it's super cold. I second medusa's suggestion of yaktrax, I just put them on right over my regular running sneakers. They are really lightweight and I have never fallen (knock on wood). That said, I don't generally just "go for it" and run through a patch of ice. I try to avoid them as much as possible. Not in Chicago but I find that all you really need for the cold (we are talking zero degrees to, say, twenty) are: running tights, a thermal top, a fleece headband, gloves, sunglasses, and a pashmina type scarf that I wrap around my face and is really lightweight. YMMV as I hear Chicago has terrible wind (understatement..)

If you don't mind treadmill running, the http://www.chicagoparkdistrict.com/facilities/fitness-centers/ are as cheap as you can get: $45-60 for three months. (Anecdotally: I run year-round, but refuse to run outdoors if there's even a little ice on the ground. Plenty of other people run on snow and ice just fine, but if you're not comfortable, you're not comfortable.)

If you're concerned about slipping, you can get http://ask.metafilter.com/69974/What-are-some-bad-weather-alternatives-to-running#1044526 or try making http://ask.metafilter.com/69974/What-are-some-bad-weather-alternatives-to-running#1044671.

I run in Minneapolis which I guess could be worse than Chicago when it comes to ice and snow. I use the Yak Trax. I also have a pair of shoes specifically for winter. Nothing gore-texy and technical, just another pair that is more leather than mesh. I used to wipe out on ice all the time during early season training for track and field in high school. It was no big deal then but now that I'm old it takes a lot longer to come back from a slam.