The men are wearing hats, the woman a scarf, it has to do with the need to keep some shade on their heads in the desert sun.
I thought that about her scarf, but, then I was thinking that having it under the chin would made me feel a lot hotter. But, then again, I just can’t stand to have anything on my head when I am working in the heat. So, I suppose it does not bother her like that.