Being a student in New York City automatically means that you are always part-pedestrian, part-dependent on public transportation. The weather in New York is pretty average, but it can get extreme during the winter, so forget leisurely strolls through Manhattan to get to class. Expect to be padded up with heavy jackets, gloves, scarves, and boots instead. Spring is a lot more bearable, although it's advisable to buy a tiny umbrella and leave it in your school bag/purse in case of unexpected showers (which you will inevitably get caught in while walking to school or back home). Summer gets pretty intense, and the city’s sidewalks don't make the heat any more bearable; however, attending school 10 minutes away from Central Park does mean that you'll be able to laze under real trees and hang out with friends in the park whenever it gets really hot.
Because most students commute to school (using the 6 train, which stops right under Hunter), they are able to avoid having to deal with the weather most of the day, since Hunter has covered bridges to get from one building to another. In other words, New York City weather is not awesome, but Hunter College students do not have to deal with it so much.