For me everyday is Day of the Horse. I wihs it could get more publicity- I have never heard of it before.
Another great option: donate to your favorite nonprofit that benefits horses. I donate to my local horse rescue - HorseNet Horse Rescue: http://www.horsenethorserescue.org
I spent the afternoon, after work with my horses. Put on new shoes, gave them new bedding, groomed and fed them. I took some of the other advise, I have a cup of coffee and watching The Man from Snowy River. It has been a great afternoon.
Oh, so today was the day of the horse and I did nothing special. In fact, I even missed out on riding because of the stormy weather. Oh well, the horses don't know any differently.
Since this country was traversed, fought for and simply enjoyed on the back of a horse, I find it more than appropriate for the horse to have it's day. Perhaps it MORE appropriate to be July 4th.