I’ll go slow here, buddy. Science is hard, particularly when you’ve trained your brain to rail against it. I’ll try to make this stuff plain - possibly to the point of minor inaccuracy but enough to enable you to grasp most of it.
Global warming, in general, causes the atmosphere - the air - to be warmer. This could mean 28º days in December when there would ordinarily be 26º days.
Warmer air holds more moisture - your lips and leathery, reptilian skin get more chapped during the winter, right? That’s because the colder air holds -less- moisture. Still, even during the winter, warmer air will still hold more moisture than cold air.
The tilt of the planet generates seasons - that’s why it’s cold during October through March in the Northern Hemisphere (tilted /away/ from the sun) and hot in the Southern Hemisphere during the same time period (tilted /towards/ the sun). In other words, during the winter, temperatures are cold enough to generate snow, even if the air is warmer from say… anthropogenic warming - all while still being warmer than they would be without it.
Guess what snow is? If you guessed “precipitation”, you’d be right. In warmer conditions, it comes in the form of rain. In any case, both are borne of… that’s right, humidity!
The cold weather in New York is generated by the tilt of the planet - so far, humans haven’t found a way to screw this up yet, so it’s still Winter when the Earth is pointed away from the Sun. The excess snow, on the other hand, comes from enhanced precipitation brought about by warmer air.
In addition to this, global warming increases the number of extreme weather events - but this is much too complicated to express over a small blog post. It can be taught fairly well in a semester of classes - which I strongly suggest you take - or at least read a book before further warming the climate by opening your mouth.