I've been hearing Disney Animation Studios more and more lately. I think this part is still up in the air. As far as that hat goes, I'd give it about a 90% certainty that it's gone soon.
I heard that a rebranding of the Studios was on the horizon as well, per Jim Hill's podcast w/ Len Testa (and from a credable source).
This would make sense since the dream that DMGMS/DHS would be a place where movies/tv shows were actually produced, and a theme park w/ rides was secondary is long, long gone... My gut says Star Wars has a major presenece at the new re-imagined studios, and with that and a focus on "riding the movies" (we've heard that somewhere else before ) comes to the forefront.
Overall with that other major changes and additions coming to WDW in the next 5-10 years, I actually like this move for DHS. There's no question that it is the weakest park right now and needs something to kick it up.
I was sitting at dinner last night and mentioned to my husband that there was a strong rumor that the hat was leaving. My husband is a quiet guy, likes our Disney trips but isn't a fan like me, and generally doesn't have much to say about it all. So imagine my shock when instead of the "is that so?" that I was expecting I got.. "What? I LOVE the hat!!!!".