I don't know what brand they use, but I seem to remember my DD getting a hot dog at All Star Movies when we stayed there in 2006. I know the hot dogs on the Boardwalk are really good!
I don't know what brand any of them are, but I've never liked any of the hot dogs at Disney--and avoid them at all costs (don't want any more heartburn on my vacation).
Thanks everyone for responding. My mom and I really like hot dogs but we are a bit picky and usually only eat Nathan's or Hebrew National. But I'm not against trying out Casey's.
I don't know if they have them at Disney (I don't like Disney's hot dogs...sorry, even if they are Nathan's), but I do know they have them at the airport in Orlando.