Rumor StatusBlue Sky
Hiro and Baymax from Big Hero 6 debuted at The Magic of Disney Animation in conjunction with the opening of their movie. It is expected that the characters will be replaced in March, potentially with an Olaf (from Frozen) meet and greet.
Often times when characters are put into the parks to promote a current movie release, the movie studio portion of the company is paying for the characters. The characters are typically only retained if the studio or the theme parks feels a need to keep them around for a longer run.
January 22, 2015: WDWMagic.com user drew81 has reported that Hiro and Baymax could be replaced with Olaf from Frozen.
January 3, 2015: @Dznycharacters on Twitter has reported that Hiro and Baymax will appear at Disney's Hollywood Studios until March.