I learned recently that cold doesn't always kill bacteria or viruses. Only heat/fire and disinfectant are most efficient, with intense heat from fire being the most sure way usually. Apparently, while ice crystals can kill some of them, most bacteria and viruses can survive in a dormant state and live indefinitely (although, there may be some exceptions). Thus, they can infect people many years down the line once they thaw. It's a good thing they're taking precautious, because it's very possible one of them could have contracted the disease depending on what they touched, how long the disease can survive on surfaces without a host, and what disinfectant methods they practice in their current era. Considering all the precautions Halberd took and what he's mentioned thus far about his work as a doctor it seems like they are pretty far along in regards to medicine advancement. Plus, the trains, gasoline tank, and rifle all suggest at least 19th century advancements in technology. Here's hoping that they did well enough to keep the disease off themselves.
With all that said, take my words with a grain of salt. I'm no expert. Just sharing what I learned recently, and I may be mistaking about some of this information or simply don't know the whole story.