The use of cold methanol is important because it is used to recrystallize or solidify the product.
Since, ice bath is also used in nitration of methyl benzoate because in this reaction the concentrated acid like sulfuric acid is used with water and it is very exothermic.
The formation pure solid from the impure solid compound by mixing with hot solvent and form saturated solution. Now, this solution as cools and pure crystal grows when solubility of the compound decreases. This whole process is called re-crystallization.
Answer: Fire requires oxygen to burn. Water "smothers" fire and prevents it from acquiring more oxygen. Fire also requires heat, which cool water may prevent/remove.
