Newspaper will defintiely help. For a more long-term solution you might want to look at one of the newer windproof jackets. I have a golite wisp. It weighs next to noghing, packs up into its pocket (about the size of a baseball) & absolutely blocks all wind. The difference between that & my old windbreaker, which was just nylon & which the wind does get through is night & day. It's amazing how something so light & thin can make such a difference in comfort. Something like that really makes your layers underneath work better.