The polarization transfer between hyperpolarized xenon (Xe) and the protons (H) of different solutes at very low magnetic fields ranging from 0.001 to 0.014 T is reported. Due to Xe-H cross-relaxation (Spin Polarized Induced Nuclear Overhauser Effect (SPINOE)) the observed proton NMR signal of liquid ethanol, butanol and toluene is enhanced at room temperature by a factor of 1000 in a field of B = 0.001 T. Smaller proton enhancement factors between 10 and 100 are measured for ethanol/water mixtures and for sunflower oil. Using high-field Xe NMR, the phase transitions of melting hyperpolarized Xe ice frozen onto the surface of ethanol ice is investigated.