How would you rule casting Leomund's Tiny Hut on a creature so large it is effectively terrain? Would the hut move when the creature moves or would it just stay floating in the air if the creature moves? 

I would let it move with the creature, with clear indication that I was erring on the side of cool for the party's benefit.

I would also allow it if the creature were large enough, but I don't think there are any official 5e monsters that are large enough to really qualify.

If it's large enough to have a 20ft diameter circle of flat ground, then I say go for it. A construct built for the purpose could be exactly 20ftx20ft, but a normal creature would have to be substantially larger, like a Primal Earth Titan, to account for the natural curvature of the body. My point of reference is a sailing ship, which has the dimensions of 100x20ft. 

See also, casting it on a ship, or any other moving set piece. 5E is fuzzy about the difference between ground and floors, just do what makes sense in your game. 

I agree with what everyone else has said, and that is how I would rule it.

But if you are looking for RAW, the spell fails if the area includes a creature larger than medium.

Well, the area is the dome in the party's square, which is above the mega beast. So I'm not sure the spell would fail, vs. just staying in place as the beast moves out from beneath it. Or, if the beast gets taller back around its rump, the dome could even stop the beast from moving in a way that would cause any part of it to enter the dome's area? yikes. 

The height of creatures squares, and whether they occupy the same square as the creatures mounted atop them, is a fuzzy concept in 5E grid (cube?) based play. 

Quote from scatterbraind >>

I would let it move with the creature, with clear indication that I was erring on the side of cool for the party's benefit.

 [emphasis added]

This is the best reply to most questions like this.

Thanks guys!