The amount of salt in water (called the "salinity") is very important for setting up the currents and flows within the ocean. Salt atoms and ions (mostly sodium and chlorine, but also calcium, sulfate, and others) are able to fit in the spaces between water molecules, and are also heavier than water molecules. This means that salty water is heavier than the same volume of fresh water. We say that salty water has a higher density than fresh water.
Temperature also changes density: hot water weighs less than cold water. Heavy stuff tends to sink, so colder or saltier water tends to sink in the ocean, and warmer or fresher water tends to rise. These rising or sinking forces (combined with some other, very complicated physics which is outside the scope of your question) cause currents to flow in the ocean.
Ocean currents are important for climate. They carry warm water from tropical regions toward the poles. If the Atlantic Ocean didn't do this, it would be much, much colder in New York where you live, especially during the wintertime. England and the rest of Europe would be even worse off.
So, to answer your question, salinity doesn't directly affect the climate of nearby land. However, changes in salinity can change the strength of ocean currents, which can make large changes in the climate everywhere on the planet.
Try the links in the MadSci Library for more information on Earth Sciences.