Chunks of ice are not very comfortable. The towel does not permit the cold to get through very well. Too much barrier.

The wheat bag is ideal, because there are no pointy bits jabbing into tender places (please try to keep your minds out of the gutter fellas) and it it already wrapped in fabric, so you don't get shock of cold against the skin and it will wrap nicely round the neck in any direction, front to back or back to front.