With regard to the environment as a whole, when is the worst time to apply pesticide to your lawn? when it is raining, or is about to rain when it is cold, or is about to get cold at the same time you apply fertilizer at night

I believe the answer is: before/after rain

Rain would create water flow that could even move bigger molecules from one place to another in the environment.
Because of this, applying pesticide before/after rain would most likely spread the substance to other area and could destroy the balance in the ecosystem.