  A uniform solidification front undergoes non-trivial deformations when
encountering an insoluble dispersed particle in a melt. For solid particles,
the overall deformation characteristics are primarily dictated by heat transfer
between the particle and the surroundings, remaining unaffected by the rate of
approach of the solidification front. In this Letter, we show that, conversely,
when interacting with a droplet or a bubble, the deformation behaviour exhibits
entirely different and unexpected behaviour. It arises from an interfacial
dynamics which is specific to particles with free interfaces, namely thermal
Marangoni forces. Our study employs a combination of experiments, theory, and
numerical simulations to investigate the interaction between the droplet and
the freezing front and unveils its surprising behaviour. In particular, we
quantitatively understand the dependence of the front deformation $\Delta$ on
the front propagation velocity, which, for large front velocities, can even
revert from attraction ($\Delta < 0$) to repulsion ($\Delta > 0$).
