I agree with everything said already. You can get nylon wind pants for $15 or so from walmart, though real waterproof rain pants may be advisable if you know it's going to be that wet. These are your shell. Under that, the NON cotton long johns. If you need more, a pair of fleece pants in between (real fleece, again not cotton). if you can't find any, look for fleece pajama pants. they are the same thing. Same thing up top... wool/poly long johns, covered by fleece (maybe several layers if needed) followed by a shell such as a wind jacket or rain jacket (or both)

don't forget underwear and socks. Target and walmart both have non cotton ones. If you can't find real winter socks, two pairs of synthetic dress socks would be fine. I wear stretchy synthetic boxer briefs from target year round. You can't imagine how uncomfortably cold wet cotton underwear can be until you've experienced it.

Also, check the hunting section, they tend to have good cheap clothes, if you don't mind camo or blaze orange. A knit or fleece hat can be found there cheap too.

NO COTTON. Also, keep your sleeping bag dry or it will go from 0 degrees to nothing