My anglo-arab and my arab both toss their heads, but it doesn't relate to their seasons.
The anglo fell 'in love' (you know what I mean ) with my RI's ex-eventer. No other horse turned her head, but every time she saw him (and she was in season) she'd try to stop by him and pee. It became a bit of a battle of wills every time we passed him, luckily (particually for the traffic) I won most of the time.
ETA, he was a terrible flirt and encouraged her by prancing and neighing at her.
My mare doesn't really toss her head, but she does grab the bit and pull her neck down. She can be a bit of temperamental c** when in season - thinking of putting her on one of the hormonal calmers like moody mare or something!
Edited to say that she also has quite a few tantrums when she's in season, rearing being her specialty at the moment. When I go to turn her out in the morning she also nashes her teeth and does these minature jump type things. Only when she is in season though!
Bridle is same bridle i always use (only bridle she's ever had, she only been broken a couple months really)
Teeth done a few months back, couple possibly need doing, so will look into that.
Bit - it is new, only had it a week, still a full cheek, but is a bit it a link / lozenge in, rather than a single joint.
She wasnt tossing as badly today, but when i first got on, kept pulling head down, turning for home, and NOTHING could turn her or even stop her, she just wouldnt stop or turn so had to jump off while moving, got back on a little further down road and she was fine!
It sounds like a combination of the new bit and her testing the water (a bit of nappiness/trying it on). I think that getting off, leading her and then remounting, was exactly the right thing to do.
Hopefully when she learns to turn from your leg, you'll have alot less of this trouble.