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When the spins on the frustrated pyrochlore lattice obey the celebrated 2-$in$-2-$out$ ice rule, they stay in a correlated disordered phase and break the third law of thermodynamics. Similarly, if the atomic ions on the pyrochlore lattice move in and outward of the tetrahedra, they may obey a constraint resembling the ice rule. We discover that a model for pyrochlore molybdates $A_2$Mo$_2$O$_7$ ($A=$Y, Dy, Tb) exhibits a "supercooled ice" state of the displacement degrees of freedom of Mo$^{4+}$ ions, when we take account of the Jahn-Teller (JT) effect. The JT effect occurs when the lattice distortions reduce the symmetry of the local crystal field, resulting in the orbital-energy-splitting that causes the local energy gain. Unlike the standard JT effect that leads to periodic long range ordering, the displacements of Mo$^{4+}$ ions are disordered following the ice-like rule. We microscopically derive a model that describes this situation by having the 2nd and 3rd neighbor interactions between in-out lattice displacements comparably as strong as the nearest neighbor interactions of standard ice. There, the well-known nearly flat energy landscape of the ice state is altered to a metastable highly quasi-degenerate ice-like liquid state coexisting with a crystalline-like ground state. Our Monte Carlo simulations show that this liquid remains remarkably stable down to low temperatures by avoiding the putative first order transition. The relaxation in the supercooled JT ice state exhibits glassy dynamics with a plateau structure. They fit the feature of a "good glassformer" very often found in molecular liquids, but that has never been observed in material solids. The high glass-forming ability of the interacting lattice degrees of freedom will play a key role in the spin-glass transition of the material.