Icing of seawater droplets is capable of causing catastrophic damage to vessels, buildings, and human life, yet it also holds great potential for enhancing applications such as droplet-based freeze desalination and anti-icing of sea sprays. While large-scale sea ice growth has been investigated for decades, the icing features of small salty droplets remain poorly understood. Here, we demonstrate that salty droplet icing is governed by salt rejection-accompanied ice crystal growth, resulting in freezing dynamics different from pure water. Aided by the observation of brine films emerging on top of frozen salty droplets, we propose a universal definition of freezing duration to quantify the icing rate of droplets having varying salt concentrations. Furthermore, we show that the morphology of frozen salty droplets is governed by ice crystals that sprout from the bottom of the brine film. These crystals grow until they pierce the free interface, which we term ice sprouting. We reveal that ice sprouting is controlled by condensation at the brine film free interface, a mechanism validated through molecular dynamics simulations. Our findings shed light on the distinct physics that govern salty droplet icing, knowledge that is essential for the development of related technologies.