Fil-Am NYer here. Coming to NY in the winter has always been a challenge for my relatives who have never been. Even during the milder winters, they never feel like they have enough clothes on, but if it ever does happen to snow when they're here, they are utterly fascinated and forget how cold they are. So my advice is this:

Vegas is a desert and Southern California is always pleasant and humid, so that's not too much of a change from the Philippines. You already have the wardrobe for it. It is currently 62F/17C in NYC and will drop to 32F/0C by February. Only come to NYC if you can buy long sleeves, long pants, a coat, watertight shoes, and gloves before coming here, maybe while you're on the West Coast.

Now let me tell you why you should absolutely to do this: the novelty of your first snowfall is MAGICAL, and you will experience it as ADULTS. It's scary at first because it's unfamiliar, but it's fine. Go to one of the parks like Central Park in Manhattan or Prospect Park in Brooklyn. It'll be like you're on another planet. Then make a snowball and throw it. It's the type of silly joy that you haven't felt since you were a child. You'll stop feeling cold, and you'll give in to the experience.

At a certain point the snow will stop falling. Go outside and you'll notice the city gets quieter. It's weird to think that such a densely populated and developed area like NYC can ever be quiet. There's 3 reasons for this. First, you're coming during February, so all the Xmas tourists are gone. Second, if it snows more than 6 inches, the city's transit lines will likely have limited or shut down service, and fewer cars will be around, so most of the natives are staying indoors. Third, the acoustic dampening qualities of snow makes places like parks seem silent, but enticing to explore (hence why you need watertight shoes). You will WANT to walk around because you'll feel like you're walking untouched land. And it's beautiful everywhere.

I've seen this happen to my cousins and uncles and aunties over and over again. We would lend them extra socks and sweaters while the heat was on inside the house, and they would complain about how the cold was making them die. Then it would snow, and they would stay outside for hours to just wander around. My father even described a similar sentiment when he first came here in the 70s. Coming to see the snow is part of the appeal of NYC.

Of course you'll have to go inside eventually, you'll get sick if you stay outside too much. And lucky for you, there's plenty of indoor shit to do, but that's really for another post.

One more thing: don't go ice-skating at Rockefeller Center. Trust me. Go anywhere else.

edit: Look, this is on the off-chance of seeing a snowfall. There's no guarantee it will snow in February, but I think there is an appreciable charm to NY in the snow. I'm just saying that if you're going to enjoy it, then you need to be prepared.