Do people in hot weather places get more varicose veins (assuming heat dilates veins) than people in cold places?

Great question! You are right that heat dilates veins but that is not a permanent condition. Varicose veins are caused by vein walls that are permanently damaged by not having enough elastic tissue in them and by bad valves. The major cause for that to happen is heredity, not hot weather.
Weather. Weather does not cause varicose veins However if you do have varicose veins symptoms may be exacerbated by warm weather and increased humidity.
Not really. The warm weather may dilate veins but not necessarily have more varicose vein in warmer area than cold area.