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Since the 1.3 update people start freezing to death if you don't have enough housing.
Sometimes faster than 4 weeks.
Colonies, which start at 3000 population, at least seem to give you enough time to build housing before they start dying.

So, besides cold, hunger and sickness, the difficult part of this challenge is having enough housing, before the waves even hit. The waves also greatly increase disease for many weeks.
First wave: week 72, 4200 people (about 1400 sick/injured)
Second wave: week 189, 10100 people (about 2800-5100 sick/injured)
Third wave: week 221, 4200 people (about 2500 sick/injured)
Fourth wave: week 300, 10100 people (about 6100 sick/injured)

If your sickness is low people naturally heal after about ~10 weeks. (a few hundred)
Hospitals each heal 60 people (every 6-7 weeks) and lower disease. You will need 4 or 5 hospitals to lower the extra disease from the wave. You might want even more hospitals for the last wave if you want to complete the game before the whiteout.

No random colonists can be found in map locations, so no Outsiders law either.

One trick to avoid people dying due to lack of housing is to establish colonies. (they take 3000 people each)
You can also ship people back and forth until you build more housing.

This Tale is a good match with the Metropolis ambition (50K population)