This topic is fairly old, but I've figured that I will put my so called five cents in, since mainly the cookies that I do are fondant covered cookies.
I like using Fondx brand of fondant to cover the cookies, as it does have a pleasant vanilla/marshmallow taste. I roll it as thin as possible, definitely much, much thinner that for the cakes and attach it to the cookies with home made caramel. This method creates an additional layer of flavour and my customers love this combination! From my own experience even the die hard fondant critics were pleasantly surprised and brought over to the say yes to fondant side .
I do allow the base/background to dry a little before attaching to the cookies and in fact I decorate it while it is drying, as this way it is much easier and gives a cleaner finish. As for the embellishments - it depends on the look that I am going for. As Julia has mentioned earlier, if they are to be following the shape of the cookie, or are supposed to be blended into the background, or the decorations that are already on then I will put it on soft, as this way I have more ability to play with it. If they are just to be put on with no additional shaping, then dry is ok.
Once I have the entire pieces finished, I often leave them to dry overnight, I will leave them on the baking sheet and lightly cover with food wrap - this way they dry enough for me to pick them up and attach to the cookie without them loosing their shape, but not dry rock solid hard.
I also find that once the cookies are bagged, they never really dry rock solid hard, the fondant is just nicely chewy. Hope it helps!