Apparently, whether or not a cow seeks out shade depends on its coat color. Four breeds of cattle, with four different coat colors were tested to see where they spent their time in the sun or the shade.
The percentage of time each breed spent in shade (standing and lying down) was: 89% for Angus (black), 81% for MARC III (dark-red), 57% for MARC I (tan), and 55% for Charolais (white). There was a direct correlation (R2 = 0.90) between absorption of solar load, by hair coat color and percent of time the heifers spent in shade. Providing shade alleviated heat stress by lowering body temperature, especially for black and dark-red colored cattle.
Reference: Gebremedhin, K.G. et al. 2011. Body temperature and behavioral activities of four breeds of heifers in shade and full sun. Applied Engineering in Agriculture 27: 999-1006.