Organic sugar differs from refined sugar in some pretty significant ways -- mainly the processes undertaken during their preparation. However, the differences end at the oven's door; baking with organic sugar should give you the same results as baking with refined sugar.
Organic Sugar Versus Refined Sugar
Organic and refined sugars differ mainly in the manner in which each is processed. The refined sort undergoes a bit more processing than the organic sort; when the former is extracted, it's essentially bleached using decolorizing agents which remove the natural molasses covering that gives the sugar its coating.
Any difference in taste may be up to the person tasting it, or the brand of the sugar. Organic sugar tends to have a "slightly milder, more pure aroma but no distinguishable difference in flavor," says author Rose Beranbaum on her website, Real Baking With Rose Levy Beranbaum. Meanwhile, Wholesome Sweeteners' website states that their brand of organic sugar retains a "mellow flavor." Experiment with different brands to find one that you like.
Because refined and organic sugars' differences lie in the means of their production, not their taste, you can substitute organic sugar for refined sugar in the same amount. If you'd normally add one cup of sugar to your cookie batter, add the same amount when using organic sugar.
The use of organic sugar doesn't affect the result of baked goods any differently in any aspect than refined sugar, according to a presentation by Nigel Willerton, CEO of Wholesome Sweeteners, Inc., which is posted at the Food and Drug Administration website. Willerton states that it should "perform identically to refined sugar in most ways."