You can put whatever you want in your vehicle, but different weather scenarios don't warrant different oil types. You definitely don't want to go with a thicker oil like 10w-40. You get less flow so your basically starving your engine longer at startup (greatly increasing wear). You're also getting less flow when your engine is warm, so it's less effective at pulling heat out of your engine and doesn't provide as much lubrication since there's less flow.

Remember, your engine runs at about 210 degrees. That's 100 degrees hotter than ambient. That's like you standing naked in a deep freezer. Drop or raise the temp in that deep freezer another 10 degrees and you'll never know it cuz it's still ****ing cold! Well, under normal circumstances, your engine doesn't know that the ambient temp is only 100 degrees colder than it is instead of the normal 110. To your engine, it's still ****ing cold outside! The difference in cooling is minimal.

Slightly less efficient radiator, less heat removed with oil, more heat generated due to thicker oil (less flow to protect your engine from wear and friction)... I have to suggest against using a thicker oil in the summer.

 

I have seen some cars in the past recommend thinner oil in colder weather. The only deviation that would make sense to me is going 0w30 in the northern climes.