Cotswold Way - possible to do a stretch on horseback?

I am in the process of planning a trip to the Cotswolds with a friend. While I would like to walk the whole way, for the interest of time and allowing for some energy on at least one evening, is it possible to do one stretch (10-15+ miles) on horseback? We are familiar with horses and wouldn't be total newbies in the saddle. TIA