Interesting question from a horse owner????
Yes horse's have hair all year round.... just like any other mammal that grows a winter coat and sheds for summer. The coat just because shorter and finer through the summer months, and longer and thicker in the winter months.
When was she clipped? It is inadvisable to clip when the coat has started to change, as you will damage the summer coat coming through and the clip lines will take longer to fade. I usually clip in May (I'm in Australia though, so this is the first month of winter here) and then keep my horses rugged and stabled at night, under lights if I am really wanting their coat to stay super short. By the time the coat starts to change for summer in around August, the coat has become thicker than a normal summer coat, but not yet a full winter, and will shed nicely into a fine summer coat. Clip during this time and you risk damaging the summer coat as I said above, and your lines will last a lot longer as the coat does not shed much at all once the summer coat has come through.