Sometimes plants do die in such cold weather as we are having in Arkansas this week. Most die when people push their luck and try to grow something that isn't hardy in their area, or when winter becomes extraordinarily cold for an extended period or shows up too early. But under normal circumstances, plants don't just sit there wishing they could go inside-they acclimate in stages.
As summer days grow shorter, plants begin "freezing acclimation" by producing hormones that slow growth and induce dormancy. By the first hard frost, they are ready for freezing temperatures, and for beginning the second stage of their preparation.
The year's first below-freezing temperatures freeze the water found between plant cells. Since there is now more liquid water inside the cell than outside, osmotic pressure draws some of the water out of the cell, where falling temperatures cause it to freeze as well. Inside the cells, the concentration of cell parts increases as more water is drawn out. The more concentrated the cell parts, the lower the freezing point. So down to a particular temperature, different for each species, the cells themselves won't freeze, and the plant will survive. Below that temperature, the plant will suffer die back, starting in its branch tips because they are thinner and more exposed to the cold. But branches are expendable. The soil and any snow cover insulate the roots somewhat; if the roots survive, so will the plant.