Our club is dealing with this issue right now. I recommend you begin with a written statement of why you have a tree on your course in the first place. Reasons for trees; add challenge to a hole, indicate line of play, provide reference point, screen out disruptive sights. Reason for removal; in-play and unfair, diseased,old, ugly, interfers with agronomy, surface root systems promote injury to players or damage equipment. Member education is a key factor. We have done multiple member presentations. Once they understand the logic you will find a growing base of support. Your may also want to develop a tree planting program. Most courses have out of play border areas which make sense for planting and creating wildlife habitats. This should help satisfy the tree lovers. I do encourage you to go slowly. This is an issue that can divide a membership. It is no fun to have a great course if non of the members can talk to each other.