They were white at home basically due to superstition or marketing, depending on who you ask...lol. Tex Schramm is the one who made the decision in the 60's. He apparently wanted the Cowboys to have a unique and recognizable look that differed from other teams and made the Cowboys instantly recognized. It also, as you mnetioned is true for the Dolphins, forced teams to play in their colors in the Texas heat (Texas Stadium is known for being crazy hot on the field in the early part of the season).
They also changed their blue uniform from the more royal blue to the darker blue you see today due mainly (many believe) to superstition. They were said to lose quite a bit in their blue uniforms and thought they were jinxed.
Even now, with the darker blue unis, many people (including the owner himself) feel the blue jersies tend to be bad luck. Even many fans think the special "retros" they wear on special occasions are bad luck. It's a silly superstition to me, but if any players actually believe it I guess from their perspecitive it's best to try and avoid one more distraction. Ironically the only distraction they seem to actively avoid...lol.