Been in February and it can be bitter - however, unlike the UK, they cheerfully continue on with piles of snow around.
Cheap hotels are harder and harder to come by nowadays. I stayed in the Roger Williams last time and it was brilliant, if a little pricer - but with 2 of us sharing it worked out OK and we were 2 blocks from the Empire State!
If you really need to save, you could consider a hostel - we stayed at Union Square on 14th and 2nd a couple of years ago and it was cheap as chips, but not the most comfy. Personally, I'd rather have my own room, or at least share just with mates.
If you're doing everything, get the NY pass
http://www.newyorkpass.com/ You get free entry to loads of stuff, discounted entry to everything else (much more than you can do in 4 days) You will also be able to pick up your tickets away from the main ticket booth in some places (Empire State and Statue of Liberty were the main ones) which can save a huge queue. It also has loads of discounts at restaurants, shops etc.
Other bits - if you're shopping, take your passport to Macy's and go to the visitors desk to get a 10% discount card. At the desk there's a huge stand with coupons for just about every attraction in NY - well worth checking out ASAP. In fact, pick up every tourist guide you see, they all carry coupons

Oh yeah - check out Century 21, near the WTC - it's like TK Maxx on steroids...
Travelling around - get a Metrocard for the time you're there, paying as you gets expensive real quick. The MTA has a map that shows manhattan overlaid with the bus and subway routes, that comes with me everytime I go
