Smartphones are fine - as long as you don't mind the potential risk of a hole in the retina. An unusual case but don't remember reading that we shouldn't be using our smartphones outdoors. I can't be imagining the pain I feel when looking at LED back-lit displays.
I am quite dubious of this, doesn't seem there is actually any evidence as to the cause.
Maybe don't look at your phone with the sun reflecting on the screen?