I used to live in Wilts. There’s not much on the flat land close to Melsham / Trowbridge and, like Daffy says, it gets churned up into really thick clag in winter. Up side is it’s not far to the N edge of Salisbury Plain, ride towards the big white horse on the hill above Westbury. There’s miles of trails including some military stuff which is open if the red flags aren’t flying. It’s also possible to join the Ridgeway with a short link on roads across the flat land E of Devizes.
Used to ride in the woods round Center Parcs at Longleat. Most aren’t public rights of way but the estate used to have a tolerant attitude.
There’s some better stuff over towards Bath as well