Do both. They are complimentary tests. The cold start answers questions about the sensors and power systems needed to get the engine going. The idle tests the opposite, how the engine handles thermal issues without the airflow of driving. But the common theme is that if the engine starts and runs, most everything else can be reasonably fixed.

In my area, people talk about only buying cars in winter. You don't know a car until you see it at sub-zero temperatures.