This answer assumes that the four trees are located on common area, and not on exclusive use common area (property designated for the sole use of one unit, such as a yard or patio).
Common area is managed by the association through its board of directors. Unless the association’s CC&Rs limit the board’s rights (which would be very unusual), the board has the sole authority to make decisions on landscaping, maintenance and repair issues. The board can decide to cut down these trees without replacing them. While the lack of trees may have the negative results you mentioned, the board is within its rights to decide that the maintenance problems created by the trees are more pressing than a reduction in shade or privacy. The board, however, is obligated to make this kind of decision in good faith after conducting a reasonable amount of inquiry, acting in what it considers to be the best interests of the association.
While the individual homeowners cannot stop the board from cutting down common area trees, you do have avenues to express your disagreement. You can demand an informal "meet and confer" to discuss your complaint with the Board or a Board representative; you can address the Board at the next open Board meeting to express your opinion; and at the next election the owners can vote for candidates who believe the trees should be replanted.
If the trees are located on exclusive use common area, the issue of your rights to the trees is more complicated. You would need an attorney to advise you after reviewing the association’s governing documents and any other relevant documents.