"How important is it to have a "breathable" hood on a garment like this?"
Well, the rest of the garment is breathable, too... sure makes sense to keep w/the pattern. Also note that the head produces a lot of sweat. Think about your sweaty areas when you're working hard: feet, groin, armpits, forehead/neck, small of back. No disadvantage to making your hood WPB. Might make it more manageable to keep the hood up in variable conditions, whereas you'd keep a bit much humidity/heat in w/sil.