"On the fourth day we had a feast" is an achievement you get when you've hunted down 20 horses by day 4.
That has only been achieved by a mere 10% of players at the time of me writing this guide. That partly explains the problems many people have: Lack of money early on.

Each deer nets you a profit of 3 coins. Reaching that achievement means you got >= 60 coins more than without hunting by day 4!

Herding is easy once you understand the mechanics.
1. walk deer down until you got a group of 2-4 together (mostly on the left side)
2. start running until you've overtaken them and they change direction towards your castle
3. walk/run them in your archers' range

Three things you need to keep in mind for that:
1. keep track of the time, don't get caught with your pants down in the middle of the forest. Also remember that your archers won't kill deer at night.
2. don't recruit campers before herding. Deer shy away from your people and will change direction again if they meet your townsfolk on their way from camp to castle. Only recruit them once the herded deer has passed their camp!!!
3. Have enough archers on that side. 1-2 archers won't kill the deer and you wasted time.

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Good hunting! Let's ramp up that achievement count!