I just posted a great review of doing Tulum on your own via ferry and bus. Here is the link to it;
The reviewer leaves nothing to the imagination.
If you decide to do the horseback riding on your own, you can take a taxi to Playa San Francisco and then walk southward down the beach towards Playa Del Sol. You will find the horses right on the beach.
Nancy makes a good point about being safe. If you speak at least some Spanish, you will be much more comfortable doing it on your own.
Let us know how it goes.