White hair commonly discolors to ivory-ish, but hair in general holds up better than the vinyl. I've heard that bagging scented ponies to make them smell stronger can turn their hair gray or brown, but I've personally never seen a badly affected pony; the lighter hair colors on them tend to be a bit "off," most often the lavender on Peppermint Crunch.
In addition to fading and discoloring, hair can also rot. It seems to be caused by excessive heat and to be an advanced form of frizz. While all colors can be affected (my poor childhood Rainbow Flash!), dark pink is more prone to it. All of my ponies with hair rot have one of three dark pink colors (darker G1 color seen on Heartthrob; lighter G3 color seen on Sparkleworks; warmer G3 color seen on Tangerine Twinkle), and on multicolored-haired ponies, the dark pink is the worst. I even have a couple whose dark pink stripes are frizzy while the rest of the hair is fine. I've seen rot being reported on a lot of Avon ponies, which makes me wonder if they were kept in hot warehouses! That's a bit off-topic, but it is a less-discussed hair flaw that could use more awareness.