This question presupposes a lot and it's a deep topic so I don't want to get lost in the weeds. Your question, I assume, is based on the idea that humans may w

This question presupposes a lot and it's a deep topic so I don't want to get lost in the weeds. Your question, I assume, is based on the idea that humans may well colonize Mars and one of reasons for doing so is to increase humanity's chance of survival an otherwise extinction-level event. It's worth pointing out that nuclear war is just one of many potential extinction level events. Even then, nuclear war in particular is unlikely to exterminate the entire species. Another where colonizing Mars would help is, say, a massive body impacting Earth. But stepping back, colonizing Mars is largely a romantic notion, not a logical one. People imagine themselves walking on Mars but there are severe problems with this: 1. Gravity is much lower than Earth. It's roughly similar to the Moon. It's unclear how we'd deal with living in low-gee like this on an indefinite basis; 2. Mars has an atmosphere but it's actually worse than no atmosphere in many ways. It's barely above vacuum so you can't breathe it, even if it was the right gas mix (which of course it isn't). All it really does is stir up dust to cover all your above-ground installations. Solar panels are likely to be one of these so you can't really avoid it. Dirt and dust on Earth have been eroded by eons of wind and water. Not so on Mars. Martian dust is jagged and "sticky" as a result. So it's more annoying. 3. Mars has no protection from solar radiation unlike Earth (ie the Van Allen belt / magnetosphere); and 4. Even though gravity is lower, getting into and out of the gravity well is still a considerable issue, particularly given the lower atmosphere doesn't have the same potential for aerobraking as Earth's atmosphere does. For nuclear war in particular, a political entity may well also exist on Mars that will make a nuclear strike. You'd likely get more warning since Earth's superpowers have quick strike capability from nuclear attack submarines that can be positioned off the coast of major cities. Mars of course has no oceans so you're talking air or ground vehicles or ground installations. Nuclear missiles could come from Earth but you'd get a lot of warning for this (weeks to months) and this wouldn't be cheap. Personally I'm convinced the future of spacefaring humans is in orbitals not on other moons or worlds.