It sounds to me, like was mentioned before, that it is a blanket law designed to cover any type of emergency. Most likely they were thinking that this law would help to stop a situation from escalating from a disaster into full on civil unrest.
I think their goal with this law was to be able to better control situations like rioting and looting. People who would normally not get involved in those situations would be more likely to if they were drunk and/or had easy access to the situation (i.e. a vehicle). Adding guns would only exacerbate the situation. Banning guns also serves to cut down on "do-gooder" types trying to go down and "help" control the situation with a gun. If someone has to walk for 2 hours they are much less likely than if they only had to drive for 20 minutes.
In this situation I think that banning driving is actually a smart idea. Driving in a blizzard is going to cause more accidents, and put even more of a strain on the already taxed emergency services.
What the government should have done was added in separate rules for each different type of disaster. Instead they chose to make a blanket law that 9 times out of 10 is going to be overkill.
On the other hand, the government may just be out to get them.
--Whitney