I brought a 20 yr old from Ireland to Italy and she has coped fine. Didn't need clipping but has a fine coat anyway. As above make sure they have shelter and plenty of water and they will be fine :)
A friend moved her mare to Dubai from the UK, she clipped her out fully before the journey and she travelled fine on the plane etc. She settled in no problem and its really hot there. If your 20 yr old is fit and well and you break up the journey etc don't see they shouldn't adapt as long as she has shelter from sun etc. Maybe move over in cooler months to allow time to settle before it gets too hot!