Like anything else, a course (particularly a parkland course), can have too many or too few trees.
Trees that choke off fairways, block air and light, and provide no choice but to be in a fairway or chip out are bad architecture. Little Mill also came to my mind when I read the first post.
But several trees set back from fairways and greens that penalize poor shots and often offer shot choices (fades, draws, low shots, sometimes punch outs on the rare occasion of a perfect stymie) are good architecture. Tree removal programs that leave a course with few if any obstacles between tees and greens, in my opinion, are not good architecture. Yes, Oakmont removed all trees, but 130 bunkers provide more than enough driving challenge. I do not believe a parkland course with very few trees works very often.