Problems

I see a few problems with naturally available substances to use as insulators for a shelter:

1. Availability. How many sheep would it take to make enough wool to insulate a house?
2. They burn. I might be wrong but I can't think of a single natural substance that has insulative properties that doesn't burn.
3. They won't last. They will decay or rot or grow mildew, etc.

Solutions?

1. Move. Once things settle down and you know what the climate will be where you are, you can plan to move if it is too severe.
2. Different methods of construction. Once the shift has passed, build in the side of a hill or underground. Build a log cabin. The early settlers seemed to do just fine in log cabins. There will be plenty of trees, some of which might already have fallen due to earthquakes or high winds. You probably won't be able to run around in your 'skibbies' inside a log cabin in the winter, but I'm sure you could make it comfortable.

Offered by Michael.

I don't know if this has been mentioned yet, but one method could be tires filled with packed dirt. There should be plenty of both laying around after the pole shift. This is used in Earthship homes.

Offered by Liai.