My mare has kinda been doing this since I got her. It hasn't gotten any worse and did get better with a chiro treatments but she'll still do it. At times when I see her running in the pasture OR while I'm free lunging her she'll swing her head side to side. And at random times while riding she'll shake her head. I was told by someone who rode her for a trail ride she needed a tie down. But I've gotten so used to the shaking when we ride It doesn't bother me. She at least does it 5 to 6 times or more while riding. She acts like she's agitated but nothing is there. She hates nose pressure or any kinda face pressure at that. She does okay with halters and I can ride in her one but it usually ends up with her shaking her head or raising it or lowering it. It COULD be attitude but I'm not sure.
(free lunging area, I have a round pen now so this went bye bye.).