We're not used to sub zero weather in Chicago. Clearly we have a frozen pipe somewhere, probably in the crawl space. My question is: if I'm getting a trickle of water from the hot faucets, where is that water coming from? Is there always some cold water mixing with the hot (which would explain how cold the trickle of water feels), or is it coming directly from the water heater (which would suggest that the pipe from the heater is not quite solidly frozen yet)? Thanks

In real cold weather I always leave my cold water faucet in the kitchen on a fast trickle to keep the lines open. If you are getting only a small flow from the hot water line, then the line is probably in the process of freezing over. You need to make sure that your hot water heater is not just pushing out water all the time as you will be wasting megabucks in hot water heating costs.

Try keeping the hot water faucet open until the water pressure increases. The water is cold due to the fact not enough hot water from the tank has reached the faucet.