Texas for the most part is not prepared for blizzards or icy conditions. We do not have winter tires, we do not carry snow shovels. There are no snowplows that I have ever seen or heard of. We close schools after 1 to 2 inches of snow, and we put sand on roads.
Most people have heavy coats/jackets, but rarely ever wear them. But despite our under-preparedness, not many people die from cold weather in Texas.
This data is a bit old(2003-2008), but is illustrative.
https://www.dshs.texas.gov/chs/vstat/Hotcolddths/hotcolddths...
I live in Houston. When it snows here we will sometimes see sand trucks driving around. They come down from North.
You can't just truck in AC though so I think your example is like comparing apples to oranges.