It will affect both taste and color of the wine, but for some wines it is required. Corn sugar is dextrose, preferred for beermaking but tradionally avoided by winemakers. Honey is another subject altogether. It comes in many, many flavors, depending upon the flowers the bees predominately visited while collecting pollens and nectares used to make it. These flavors do affect the wine, but so does the honey itself.
Honey tends to mellow out a wine and contributes ever so slightly to body.
Some people prefer it for that reason alone, while others prefer it for ecological reasons. My problem with honey is that it slows down the clarification process considerably. Honey contains pollen, and pollen takes a long time to settle out. Even when settled, it can easily be lifted from the lees by the siphoning action of racking, and then it must again settle out. If you filter your wine, this is much less a problem than if you don't.