If we are just talking about ice formation and not the point at which the whole thing freezes, then I would expect there to be many systems where the hotter ves

If we are just talking about ice formation and not the point at which the whole thing freezes, then I would expect there to be many systems where the hotter vessel would form ice quicker when put in a very cold environment. Heat being essentially kinetic energy averaged, the greater the initial energy compared to the available drop, the faster it is for large variations to develop.