The conical hats you’re talking about are known in Vietnamese as “ nón lá” or quite literally “leaf hat”.
While not so common in large cities such as Saigon which are rapidly developing and modernizing, these hats are a common sight in the countryside where they are most stereotypically worn by farmers working in their rice paddies.
As they are very cheap (about 5000 Dong or $0.25 cents or less), lightweight and offer good protection from the sun and rain, they are well liked.
Photo of me with my nón lá while I was working in Thanh Hoa Province over the Summer of 2018