That's interesting. I didn't know they migrate, but it's logical.
If it's definitely not related to feed(ie too much energy for winter lifestyle), other possibilities are lack of exercise - is the horse locked up & only gets exercise when ridden or such? If she only does it under saddle, then it could be down to saddle fit, going with weight loss over winter. Could also be nutritional deficiency - eg. Magnesium deficiency is linked with nervous behaviour & most horses that have adequate green pick will get enough Mg in their diet, but in winter...
She doesn't get as much exercise as in the summer, but she spends out the whole day, so she can move as much as she wants. I'm not 100% about the saddle fit, but she starts acting up before any changes in her weight and she's not crazy when I ride her at home. She's 'bad' only on trails and on lunge in canter.
It's good to know about Magnesium. I didn't give her any vitamins, minerals (she has the salt block, but she doesn't touch it in the winter) so this is a thing to fix. I'll definitely give her vit/mineral mix this year, as soon as grazing is over.
I guess I won't try alfalfa and risk even crazier horse. More beet pulp and oil should do the trick, without too much energy.
And lunging before riding like Tinyliny said, if magnesium won't do the trick.