The odds of actually seeing one of these trains, much less being on one, are extremely low. While they do publish a schedule, it's pretty much limited to "the train will be on the Blue line on Saturday". EL lines are long, so the train probably only makes a few round trips the entire day. I only got on one once when I was waiting for my train near the beginning of the line and saw it pass in the other direction. I waited a couple trains and sure enough it came back around, but that was the only time I've even seen one of them.

That having been said, Chicago is GLORIOUS at Christmas - lights on North Michigan Avenue, all the stores decorated, everyone out shopping. You can do the Nutcracker ballet or go to the Goodman for A Christmas Carol. Sure, it might be cold but that's part of the fun.