I have just come across this thread.
Carole, you are too kind.
As I understand it you are looking for a climber that is drought tolerant, frost hardy (how much frost?) and that flowers in spring or autumn. Do you have any preferences for colour or, conversely, colours you don't like? Would you like the flowers to be scented? Firstly, I would advise taking a look at what others are growing in your area or even slightly higher up the mountain.
Carole has already mentioned Clematis, perhaps I could suggest you take a look at:
Campsis radicans
Podranea ricasoliana
Trachelospermum jasminoides
Jasmine sp
Stephanotis floribunda
Clerodendrum x speciosum
Thunbergia grandiflora
Wisteria sp
to mention just a few.