Yes it is true. Horseback riding is listed on park website https://www.mass.gov/locations/wompatuck-state-park It is also listed on camping reservations so there may be setup for horse camp sites. If you can not find out information online I would drive to ranger/visitor center and get more info or grab a map there if it's closed. Try calling. Would be a beautiful place to horseback ride! https://www.reserveamerica.com/explore/wompatuck-state-park/MA/32628/overview
I am not sure about horse trails. There are quite a few horse farms within a mile or two so I think it is likely, but I will have to defer to you asking/confirming with the D.C.R.
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