Yes, the chance to contract diseases would need to be very small. This would also make a little bit of work go further, since you could potentially play a long time without seeing them.

What Ibrahim's talking about would be fantastic if it can be done. Didn't Xenophon write about frostbite amongst the 10k when they went into the Caucasus? You could name that in proto-Germanic, Hai, and Celtic and attach it to appropriate regions.

Even better, you could make it so that the chance of getting frostbite increased dramatically when your troops were at -2 or -3 morale due to starving in foreign territory. Then foraging would get even better, representing wilder peoples abilities to deal with extreme conditions and disadvantaging urbanized soldiers who were campaigning out of their element.