I brew in a partially open shed, and whirlpool with a pump while chilling to increase the efficiency of the chiller. I don't use a lid. Haven't lost a brew doing it this way.
Have lost brews to infections when doing it outside, though whether it was during the chilling or due to un-related sanitisation issues, it's hard to say.
It's up to you and what you feel comfortable with. For a while I was super paranoid about DMS, so I was worried about covering it while temps were still above the DMS production range. However, if this were a a real thing then every no chill batch ever would have had DMS, so I'm probably over thinking it.