It's possible, but unlikely that there will be snow in the first week of March, unless you're talking about going up to Vermont or Maine. Usually the weather in NYC/Boston is in the low 40s around that time, though you won't know what you're in for until a few days before.
Don't bother buying gear. At most, make sure you have wool socks and warmish footwear (as in, no Converse). Go ahead and buy long underwear if you're planning on wearing jeans or slacks all weekend. You might not even need them, so don't spend money just because you're freaked out! Bringing a good sweater will let you get away with whatever jacket/coat you have. In general, layering is your friend, so as long as you have long sleeve tshirts to wear under your clothes, you should be fine!