This is the coldest/snowiest winter in years. Check with the weather. You will need a thick coat, scarf, hat, etc.
By default, I think they still use passport. Then look at experience. Americans with international experience is good. Foreigners with international experience (a Chinese working for Johnson & Johnson in Shanghai or a Chinese working for Goldman Sachs in Hong Kong) is good. a Chinese national with a H-working Visa working for Morgan Stanley is also good because this person has well-known/top working experience and has less Visa risk.
Dont' worry, you will have a lots of chinese classmates once you get to the school. Many US applicants are actually Chinese or american borned chinese. I think Stern is trying to diversify his student body by admitting relatively fewer people from mainland chinese because many applicants in US, particularly in great new york area have already had chinese background.
BTW, enjoy your two years in New York. Soho area is one of the most fun neighbourhood in NYC. There is a great Sichun restuarant offering the most authentic hotpot fish (Shui Zhu Yu) of entire US in my opinion. And its closeby wholefoods store is the most crowded grocery store I've ever been!