The start of chapter 4 is certainly challenging, but it is doable. The most important thing is to be very careful with your recruits. It's winter, so your farms aren't generating much food, so don't build too many soldiers early on or you won't be able to feed them.

I find it easiest to leave a soldier outside of Treverorum to guard against advance from the south, then take the bulk of my army east, building a fort outside of Confluentes as a staging ground before moving on.

Since food is scarce, a fishery is a great first upgrade, and getting the hunter upgrade for your troops is helpful too. Once you complete the Pinned Down quest, you'll get 150 wood and 150 recruits, so that will help too. If you need more recruits, remember that you can disband slaves in cities to convert them into recruits.

I don't really understand what you're saying about losing logs, though. Can you explain what's happening there?