Why is that?
The Church has encouraged people to have a minimum of a 72-hour kit (typically a backpack or backpacks with everything your family would need for 3 days away from home), as well as storing as much water and food as is possible in your circumstances, ideally a year's supply.
For example, when I lived in Idaho Falls, many of the Mormons I knew had thick concrete shelters in their basements, massive amounts of dried food prepared, huge jugs of water stored, and regularly did drills with other members of there community. Additionally, Mormon churches are usually pretty visible (plus, they'd probably be willing to take you in) and common enough that it shouldn't be too hard to get to one.