Current Liberal Studies freshman here.
Yes, all freshmen in university housing are required to have a meal plan. For Brooklyn, you have to enroll in the Brooklyn 1300 meal plan (there’s no information on what that really is). Freshman year, roommates are assigned randomly by NYU based on diversity.
The first few weeks it’ll feel like summer camp, and then it hits you when your first paper or test is assigned. The biggest shock for me was the amount of freedom I had; there’s no curfew and since neither of the campuses are closed, you’re right in the city. You have a whole week before classes begin to make friends, so just go to the Welcome Week events, talk to people on your floor, start joining clubs, etc.
You don’t register for classes until June/July. Be patient, your academic advisor will email you soon with more information. The difficulty really depends on the professor and how they grade/prepare the course, so RateMyProfessor will be your friend when registering.
Money: it depends on how much you eat out, buy groceries, go shopping, do fun things that cost money, etc. It is NYC, so you want to budget on the higher side of things. [This thread](How much do you spend per week at NYU? - New York University - College Confidential Forums) is kinda dated but useful.
Winter: it’s cold and it will snow at some point. You’ll want a good puffy coat (don’t worry about fashion), gloves, scarves, and hats. You can use rainboots as snow boots if you don’t see the point in buying two pairs of weather-related boots or can’t spare the money, but snow boots usually have more insulation that can be nice when it’s cold out. I recommend Columbia; their OmniHeat technology has gotten me through five Indiana/Chicago winters and it works for New York. Also, invest in a jacket for chilly weather because it’ll start to get cold fast and won’t warm up for a while, and you don’t want to be walking around in a parka because it’s too cold for a sweater but not that cold.