I don't have shade here. I think my cows would seek out places where there is a free circulation of air rather then look for shade. Some years back, my brother and I did lease a couple of pastures that had deap draws and some trees. Sometimes the cattle did stay in the shade during the heat of the day, sometimes they were on the hill tops. We did not see any notable difference in preformance there than here at home.
Cattle most likely seek out an environment similiar to where they were raised. From my observations, I believe the same is sometimes true of the plants and grasses they select to eat. We have bought cattle that were raised in other areas, with different plants and grasses, it appears that sometimes they graze plants that my home raised cattle would not touch. Often they do not do as well until they have been in my environment for a year or so and have been accustomed to what grows here.
That is just my thoughts, but I really don't know.