Would "o meu chapéu de verão" work in Portuguese? If it does, then "my summer hat" should be for that, shouldn't it? IMO "o meu chapéu no verão" should be "my hat in the summer" unless the other thing above is simply not used.
Este é o meu chapéu no verão (this is my hat I use during summer)
Este é o meu chapéu de verão (this is my summer hat), that means, you could use in another station even if it is not summer.