who is the rider of the horse on the satue in durham market place?

Answer 1

It is the Third Marquess of Londonderry and St. Nicholas Church, Charles WIlliam Vane-Stewart. (1778-1854)
The Marquess of Londonderry’s, whose full name was Charles William Vane Tempest Stewart, owned collieries near Durham but is principally famous as the builder of the Durham coal port of Seaham Harbour which he founded in 1828 as a rival to Sunderland.

Additional info about him: http://www.npg.org.uk/live/search/portrait.asp?LinkID=mp02783&rNo=0&role=sit