This is a very interesting and common question, and there is a little bit of research available to help guide recommendations.  The first thing to consider is that sometimes, unpredictably, a horse will have a severe, immediate response to the vaccination such as anaphylaxis.  Obviously, being ridden when this occurs can worsen the situation, and would put the rider at risk if the horse were to become weak or wobbly, or even fall.  If you are going to ride the horse after a vaccination, wait at least 30 minutes to ensure these immediate adverse effects are not seen.  Some clinicians feel that if the horse is ridden lightly after a vaccination, they develop less stiffness at the injection site.  However, it has been shown that extreme exercise (for example, galloping sets or race training) in close proximity to a vaccination can reduce the horse’s ability to respond to the vaccine appropriately, therefore the vaccine may be less effective.  It seems the exercise essentially acts as a form of stress that reduces the horse’s immune response to the vaccine.  The bottom line—while it may be safe (or potentially beneficial) to exercise a horse lightly a little while after a vaccination is given, avoid strenuous exercise.