Being an “alpha” has more to do with self image than physical size. If you approach a horse firmly believing that you are the alpha in the situation, you will have a much better chance of convincing the horse. One of the tricks I have learned over the years is to use my “drill sergeant’s voice”, which is deeper and more commanding than my usual voice. Most women have voices that are naturally higher than men’s voices, and my normal speaking voice is at the high end of the normal range, so deepening my voice and using a commanding tone that says I expect obedience and will have it NOW makes a huge difference. Your large horse will see you as lower in the pecking order until you dominate him with your mind.
I end up with a lot of stray cats, and one of my favorites is a little 4-5 lb. female, who is the smallest adult of all the indoor and outdoor cats. But she sees herself as being an alpha, and the other cats accept her image as reality. When one of the larger males approaches her, she fluffs up her fur and growls and hisses, and so far the larger cats have always backed off. I call her 60 lbs of cat in a 6 lb. body. The problem is at least in part that you don’t see yourself as being higher in the pecking order than your horse because he is so much bigger than you are. Pecking order is not established by physical size, but by self image. The leader in a group of horses in a pasture is not always the biggest horse, and once leadership and pecking order have been established, usually the head horse does not have to defend his position physically, as long as he dominates the other mentally.