A spare bike although nice is certainly not needed. I like to ride my nice bike year round and I built it to be able to handle year round commuting. Your felt is a pretty nice bike as well and could easily handle the elements with a few simple precautions. I would get full coverage fenders for sure, along with that make sure to keep the drivetrain clean and well lubed and you will be fine. Living in Chicago you really do not have to worry much about rim wear so that is not much of an issue.

You may want to re-pack your hubs with a quality water proof grease going into winter but if the bike has a lot of miles that is probably not a bad idea anyways.

In my experience if you take care of your stuff worst case you might need to put new cables and housing on the bike at the end of winter and possibly a new chain but even then you come out cheaper than fixing up your other bike and you get to ride the bike you love all year and isn't that why we do this? To be able to ride the bikes we love more?

Ride the felt, its a cross bike, it was built for horrid conditions!