I've also wondered about this. I have some down from thruhiker and I think I may try an experiment. I'll post the results.
Wool and hair are alpha-keratin, which is chemically and thermally pretty stable due to its helical structure and extensive disulphide linkages, so it can tolerate harsh chemicals and high temperatures. Down is beta-keratin, which has a wavy, sheet-like structure and very few cysteine cross-links, so it is much more sensitive to thermal and chemical damage.
I'll get some dye from Prochemical and, in a few weeks if I can find the time, I'll test the loft of the thruhiker down before and after dyeing and check out the plumes under the microscope.