You need either a big adjustable spanner and a headset spanner, as you need to hold the cone nut while tightening the locknut OR you can use some channel lock pliers on the lockring and a wrench. The latter will likely scar the nut a bit, but for a beater city bike, it doesnt matter.
Use sh*t loads of grease after disassembling and cleaning. If the bearings are caged, note this and remember to not install them upside down.
Then get a set of proper mudguards for next winter and youll spare having to do it again.
Thats all assuming its the headset--which is usually rather quiet even if its adjusted wrong or contaminated.
Park guide:
http://www.parktool.com/repair/readhowto.asp?id=127