Near-band-gap photoemission spectroscopy experiments were performed on p-GaN and p-InGaN/GaN photocathodes activated to negative electron affinity. The photoemission quantum yield of the InGaN samples with more than 5% of indium drops by more than 1 order of magnitude when the temperature is decreased while it remains constant for lower indium content. This drop is attributed to a freezing of photoelectron transport in p-InGaN due to electron localization in the fluctuating potential induced by the alloy disorder. This interpretation is supported by the disappearance at low temperature of the peak in the photoemission spectrum that corresponds to the contribution of the photoelectrons relaxed at the bottom of the InGaN conduction band.