The event that halves the productivity of your cookhouses (happens at 7:30 on the dot at day 30 something) doesn't trigger if you have dismantled (or partially dismantled) your cookhouses. If a cookhouse is still standing, it will even occur even if no-one is employed there.

The event that requires you to supply wood for your citizens scales depending on how many houses you have built. If you have built 2 houses, you will be required to pay 2 * 20 wood. If you have built 10 houses, you will be required to pay 10 * 20 wood. (It may work differently for a very large number of houses). Houses being dismantled are not counted in the number of houses the game thinks you have. So put all in a state of dismantling except 1, and wait for the event to trigger (exactly 7:30 on day 33). You will then only need to cough up 20 wood. However, if you don't have the wood required, then the game will give you a 48 hour promise (it says 24 hours, but this is a typo). If you fulfill this promise, you will get a hope bonus equivalent to 4 small promises, or 2 major promises. So what you should do is: set all houses to a state of dismantling except 1, and place as many medical posts around as you can. The event will trigger, giving you a promise to get 20 wood. Undo all the medical post builds, and put all your houses back to normal, and the game will give you the hope bonus. Bear in mind that the hope bonus will happen the moment you get the amount of wood required, so if you want to save the promise to be fulfilled until a bit later, it is better to make the people ask for a large amount of wood.

The game makes it easier for you after the third wave of refugees. You will no longer get housing based dilemmas, and the dilemmas based around healthcare get significantly harder to trigger. The game also increases temperature by 2 levels for a short period of time when the third wave arrives, which is not shown on your weather forecast until it happens.