The horse suddenly throws its head vertically and strikes out with a front leg at the same time. On removal of the bridle the horse always seems to have a very itchy and sensitive muzzle and wants to rub a lot. They also usually sneeze a lot when ridden. You can help the situation by using a nose net. This is basically a piece of thin mesh material e.g.,a lady's stocking which goes around the horse's nose from the cavesson noseband .
Some people hang a fly fringe on their horse's noseband when riding which also works sometimes.
There are some herbal, homeopathic remedies available in this country too. It would be interesting to know whether head shaking is recognised as a problem in your country too. It seems a recent problem here and may be to do with all the extra agricultural sprays etc being used. I hope that the solution to this problem is found in your horse's mouth, as the head shaking is a nuisance and once horse's start to suffer from it they do not seem to get rid of it. Finally ,if you are getting a lot more Spring grass than normal it would be worth moving him or limiting grazing just to eradicate that particular aspect.