According to the research published in Journal of Comparative Physiology A, gray squirrels (Sciurus carolinensis) can differentiate green, red with other colors but not able to distinguish green with red. This symptom is called dichromatic color vision. (Reference: Are Squirrels Able to Enjoy the Changing Colors of the Fall? C. Claiborne Ray, The New York Times)
That being said, the squirrels can not enjoy the fall colors of trees but can differentiate the trees with the environment.
From our observation, the most active time for the gray squirrels around and on our pin oak trees are early morning (before 8 a.m.) and late afternoon (4-5 p.m.), when the sunlight is not that strong. On cloudy days, they will more likely to show up than very sunny days, which further proves their resistance to strong sunlight.
However, our pin oaks would prefer a full sun environment to grow, which means at least 6 hours of direct, unfiltered sun, according to the tree guide by Arbor Day Foundation.
As we all know, the pin oaks can provide great sun shading, that blocks the sun for the gray squirrels. This is one of the reasons why these two are good friends in addition to the squirrels’ needs of collecting acorns from the trees.
The One Tree Project 