The animals usually take pretty good care of themselves. The find shelter in the bush and ride it out pretty well.
I had a cat that took off as soon as the winds started before Hurrican Bertha and she came home the next day, no worse for wear, just hungry and a little wet.
It is really interesting to me how animals will start finding shelter or herding together before a storm. You can almost predict a storm by watching their behavior. I bet they do just fine--I hope!
You'd be surprised how well they react. They are usually preparing ahead of us. From what I gather, their senses are much more susceptible to the pressure decreases.
The Tsunami in SE Asia saw very few animal deaths. Most made it to the hills well before the surge.