It would depend upon your view of the change, but at its core you are correct. [It's not like he can't continue to be an overlord of ice just because he's somewhere new. Well, assuming wherever this new place is has ice but yes, obviously this city does. The comparison between the frozen treat and the element causes him to snort, but it's almost out of amusement.

The invitation though has him moving forward, opening the door for the other man.]

If we are to fulfill this obligation handed to us by those operating under the will of the demon Rosier, we must.