Most LED string lights are weatherproof and shatterproof with energy-saving bulbs that glow decently on less power consumption.  So while you can leave them on all night, it's better to turn them off to conserve energy, prevent sparking a hazard (if something goes wrong with the circuit or if the wire gets chewed by animals at night or early morning) or to simply be considerate towards the fellow campers who want to enjoy the starry nights but are unable to do so because of the brightness coming from your campsite. Consider using string lights with a timer or use solar-powered string lights so that is switches off automatically.