Hi there, so we have been dry laying travertine and marble the last few years on patios and even on driveways. In fact, my own driveway has travertine with a marble soldier course (border). The only issues we have seen has more to do with the grain of the stone and less so the weather. We have had some cracked stones due to the way the veins of the stone laid out. I have seen this with tile too. So the short answer is it holds up well but be prepared to replace a few stones the first couple of years. If it is dry laid it is very simple to do and if we installed the patio we would do it at no charge. I think the very few cracked stones is worth it. It is beautiful as you can see. I can send you some more pictures of other jobs including mine if you like. Good luck!