Cheap all-season tires that are good in snow?

My current front tires are 205/60/R15 Assurythr? supergaurd Z rated tires that are really old, Lincoln's Head sticks out when I do the penny "trick" to check tread depth, and the tread is directional for rain repellentation. When I tap the gas pedal in rain my tires spin easy and don't gain traction for a while (and it's only a 95' Accord V6).
I don't think there's any way I can get the car to drive when it snows in a few days in NYC. I'm thinking about a couple of all-season tires now based on the tread design (that looks good for snow) and price.

Firestone FireHawk Indy 500 (http://www.tirerack.com/tires/tires.jsp?tireMake=Firestone&tireModel=Firehawk+Indy+500)
Fuzion HRi (http://www.tirerack.com/tires/tires.jsp?tireMake=Fuzion&tireModel=HRi)
Sumitomo HTR H4 (http://www.tirerack.com/tires/tires.jsp?tireMake=Sumitomo&tireModel=HTR+H4)
Falken Ziex ZE-512 (http://1010tires.com/tire.asp?tirebrand=Falken&tiremodel=Ziex+ZE-512)

Thanks!

Holy crap. It just snowed like centimeter or two early this morning and I took my car for a test drive.
I couldn't stabalize the car above 25 mph no matter how easy I was on the pedal the front end would sway left/right. I couldn't brake at all even at 10mph slowly I had to pump the brakes like crazy.
I turned on my ABS and the abs clicks a lot while braking.
My rear did not fish tail at (because my drear tires are non directional treaded HP50's?) all when I was turning at 15-20 onto an avenue, my front did and I had to pull the hand brake to straighten out my car or I would've hit something lol.
Wow Thank G-d I'm not goin to college till monday cause there would be no way I could drive faster than 25 with these tires without crashing.

I can't say anything about snow, but I have 195/60 Falken 512s and they did good in slush and well in rain.

Just get tires that are rated M&S for mud and snow. And do it now and do all four tires. It is not necessary to get the most expensive tires. I always go for ones that are 50-60 thousand mile tires.

Well I went to my tire shop and I got two Falken Ziex ZE-512 for $135 with install and alignment. That's not bad since sears charges $67 w/o anything. I payed a down payment should be getting them in 30 mins.
It's ganna snow tonight hopefully they'll do good in snow even though they are directional.