It doesn't realy matter, the wood might be dry, but the moss is damp.. Cyanoacrylate needs moist to cure, in normal sittuations it will set because the air is always slightly moist or the material is. If all is dry to the bone this stuff takes a long time to finaly stick. Excess moist will make it cure much faster and make it turn white, that's what the damp moss will do, no getting around that.
Best is using the gell type glue and work with tiny dots, if you have longer strings of moss just put a tiny dot at each end and press it in the glue with a tooth pick and be realy fast. Finaly the moss will attach anyway and grow on if it likes that spot.. This kinda depends on kind of wood and it's age (under water) and kind of moss.. I have some taxiphyllum moss not willing to attach to certain places the same piece of wood it just lets loose on it's own like it is growing away from it and attaching somewhere else i didn't put it. But this process can take weeks or months.. Nothing much you can do if it doesn't want, than let it go it's own way, you can't force it. Decorative fresh wood like opuwa, mopani and spiderwood that never has been under water needs time to soak, age and soften. If you want garantied succes let it soak a few weeks/months before putting moss to it and in the aquarium.
The white spots of glue will dissapear on it's own in a few weeks, it wears off. By the time the moss likely will be attached or not. 🙂