I installed a heat lamp in the goat shed and put up a tarp barrier to create a little room that would (hopefully) retain some heat. Turns out the goats are afraid of the heat lamp and would rather sleep on the other side of the tarp, so that effort was a bit of a bust.
The chickens have their own heat lamp in their coop. It keeps them warm, but I'm pretty sure the light also keeps them awake. I've noticed some drowsy chickens in the barnyard during the day. Hens with large combs are in danger of frostbite. The solution is to rub Vaseline on the sensitive area. I can attest that smearing Vaseline on a chicken is just as hard as it sounds.
I read up on cold-weather livestock care on my goat and chicken forums, and also talked to other animal owners (including my friend who grew up on a farm outside Chicago, where it gets SERIOUSLY cold). The general consensus is that these critters are really hearty, and will be just fine.
Nonetheless, I will feel so much better when it warms up!