We report on experiments performed with droplets of supercooled liquid ${\mathrm{H}}_{2}$, maintained in a state of neutral buoyancy in pressurized $^{4}\mathrm{He}$ fluid. We have measured the nucleation rate for solidification as a function of temperature, and have observed and analyzed several interesting hydrodynamic effects relating to the motion of the drops and interactions between them. We discuss the possibility of supercooling liquid ${\mathrm{H}}_{2}$ to sufficiently low temperatures to observe the superfluid phase.