That would be an interesting court case to read - but I suspect they'd not make the argument - trademark is not blanket, its for the purpose specified - so merely copying or redistributing the work wouldnt trigger it, unless you try to use it to promote animation works or similar.
OTOH, Disney is aggressively pushing trademark where it hasn't gone before. For example, they're asserting that "Movies about Snow White" are a thing only Disney can do, because "Snow White" is a trademark.
I could absolutely see Disney saying "That clip of Steamboat Willie is a trademark of Disney Animation Studios. If you use that in animation, you're diluting our trademark."
By the time the movie enters the Public Domain, Disney will be able to defend the clip with a trademark defense.