yes true - but partly,,, a lot depends on the base oil viscosity index (not the W numbers printed on the bottle) - the VI is found on the TDS of the product, a higher VI indicates less change of viscosity between temperature swings.
now lets take a 20W50 havoline motor oil which is the cheapest liquified dinosaur juice available right now, it is multigrade but when I put it in a mehran and take it to umm lets say some glacier up north, the stupid thing refuses to start as the oil is now thick as glue, OTOH, If I fill up the mehran with a 5w20 lube and aim for the arctic weather, it will start easily (provided its not acting like Pak suzuki everywhere else like handles breaking off due to freezing)
This 5W20 lube whether its marketed by the glitzy synthetic name or ground up dinosaur name - it does provide advantage for cold start.
Now speaking of the higher number (aka hot viscosity) - its not just about spirited driving or about performance engine, its how the engine was built in the first place, the bearing clearances, any other devices requiring immediate and high flow requirements, oil sump (dry or wet) or even local extreme heat (turbocharger cartridge)
You saying that all engine temperatures are the same whether the engine is in the arctic or in the thal desert,, true but also take into consideration about cooling - a car driving in chill of -20C will have no problems of overheating, the coolant thermostat will probably be shuttling between close and mix 90% of the time, airflow over the sump will cause the oil to cool down extremely quick too. If you go exact opposite on this situation you will then get a clearer idea of the "delta" difference I posted earlier. The reason different oils are specced is majorly to give the engine a fighting chance to deal with the heat stress its being presented.
Just like the forklift example I gave, you cannot use arctic spec oil in the same engine (unless the engine is designed such to use really thin lubes) in the thal desert. Your engine will suffer film strength issues on the bearing surfaces, this is where an oil with high temperature high shear stability counts.