We use an excellent Equine Vets near Llandeilo, they cover a wide area, have facilities for operations there as well. The Brechfa Forest area is a good area for horse riding, the land there tends to be poorer though...
Do research the riding, I have many friends who moved to Wales expecting there to be amazing riding, sadly most have been very disappointed. Bridleways on the OS map often don't exist on the ground, unrideable etc - worth speaking to people that live/ride in the area that you are looking at to...