Symbol fonts cannot be used in logo, illustration or button/icon designs. They’re considered stock art (similar to Adobe brushes) and must be declared like stock in contests where stock content is allowed.
Like any other fonts, Wingdings, Dingbats and other glyph fonts can’t be copyrighted unless they’re created or altered uniquely by designers.
Some of the glyphs in these fonts — such as the recycle symbol — are obviously in the public domain and are able to be used, but they cannot be copyrighted or trademarked unless they’re heavily modified, and/or are part of a larger design.