Motivated by the occurrence of a moderately nearby supernova near the beginning of the Pleistocene, possibly as part of a long-term series beginning in the Miocene, we investigated whether nitrate rainout resulting from the atmospheric ionization of enhanced cosmic ray flux could have, through its fertilizer effect, initiated carbon dioxide drawdown. Such a drawdown could possibly reduce the greenhouse effect and induce the climate change that led to the Pleistocene glaciations. We estimate that the nitrogen flux enhancement onto the surface from an event at 50 pc would be of order 10%, probably too small for dramatic changes. We estimate deposition of iron (another potential fertilizer) and find it is also too small to be significant. There are also competing effects of opposite sign, including muon irradiation and reduction in photosynthetic yield caused by UV increase from stratospheric ozone layer depletion, leading to an ambiguous result. However, if the atmospheric ionization induces a large increase in the frequency of lightning, as argued elsewhere, the amount of nitrate synthesis should be much larger, dominate over the other effects and induce the climate change. More work needs to be done to clarify the effects on lightning frequency.