The good thing about weather in New York is that there are four, distinct seasons. In the winter it is very cold—sweaters, long coats, hats, gloves, and scarves are a must during this time. Winter also seems to go on forever, so be prepared for those long, dreary months and dreading going to class because it's so cold outside. There is a rumor that Columbia did an experiment that proved the intersection of Broadway and 116th Street was the windiest intersection in all of New York City. Spring and fall are the nicest times with the most moderate temperatures, although people from the South and California may still find these seasons a little bit chilly. Summer tends to strike without warning during reading week or finals, which makes sitting inside studying or taking tests next to impossible. Summers in New York are very hot and muggy, though, so make sure warm clothes are not the only thing that you bring. You should also bring a fan, since most buildings don't have air conditioning.
New York tends to have decent weather and normally doesn't have temperatures that are too extreme, but the weather is so unpredictable that it is hard to enjoy. You have to change clothes sometimes several times a day to keep up with the changing weather. Also, there are more than a fair share of dreary, gray days, which make for a very "big city" type of atmosphere, but it can get old quickly.