Question

Why can't yeast reproduce in a cold temperature ?

Answer 1

Temperature is probably the most important factor in controlling your yeast. Cooler temps will lead to relatively slower metabolisms, and thus less rapid fermentation.

At low temperatures (0-10 C) yeast will not grow, but not die either. At temperatures 10-37 C yeast will
grow and multiply, faster at higher temperatures with an optimal growth at 30 or 37 C (that depends on the species). At higher temperature the cells become stressed, meaning that their content becomes damaged and which can be repaired to some degree. At high temperatures (>50 C) the cells die. The bacteria can survive freezing under certain conditions.

The main reason is the ability of the enzymes that catalyze all the biochemical reactions in the yeast cell to function at those temperatures. Enzymes have an optimal temperature range. When you get below that range their ability to catalyze the intended reaction really slows down. Above that temperature and the enzyme begins to denature or unfold and becomes inactive. Each enzyme will have a different range where it becomes inactive.