The David trilogy made me wonder about morphs aging actually, because as it stood I don't see how a 13 year old kid as intelligent as David seemed to think he was, could think he could keep morphing a 15(ish) year old for years and not have anyone notice he isn't getting any older, yet no one pointed this out to David so I wondered "hey, maybe the morphs age while you're in them" but that didn't make any sense really since essentially once you morph out you discard any changes made to the animal, i.e. their injuries aren't there the next time you morph, why would any time passed in that body affect them?
There's a lot about morphing that we just have to guess about, but when you really think about it you should be able to morph a winter coat, it's in the DNA. Of course if Rachel can't revert her hair style back to normal (at one book, I think 2, she mentions that she got a bad haircut and wishes that morphing could fix it, then states that it can't) I doubt you can really dictate how the animal will look when you're done, it's just going to be exactly as it was when you acquired it.