I believe damask is normally woven face down. This is what I have done so far, but occasionally I do mistreadle, which causes long floats on the face of the cloth, which if woven down I do not see until the cloth is off the loom.
I am about to embark on weaving silk damask yardage. A friend who weaves, but does not weave damask or on a double harness loom, advised me to just weave it face up. I have woven a sample face up and there are some difficulties with the pattern shafts falling when switching. I would like to hear thoughts of more experienced drawloom weavers, before I make my decision.