I am not aware of any reason why it is necessarily illegal, but it raises a lot of questions, particularly under state law. You don’t say whether the donor is a member of the board, but in many states the nonprofit corporation law permits only directors to serve on committees that make decisions for the organization.  There may be an exception for the investment committee that allows the corporation to appoint a qualified financial adviser, even if not on the board, to an investment committee.  It may depend on whether the committee makes decisions or merely makes recommendations to the board. You have to check your state law to see if you can accommodate your donor.

You also have to be concerned about whether you are creating a donor advised fund by allowing a donor to make investment recommendations on funds that he or she contributed.  We normally think that DAFs are created by giving the donor the right to advise on the use of the funds, but they can also be created by allowing the donor to advise on the investment of the funds.  (See Ready Reference Page: “Congress Passes Charitable Reforms.”) There are a number of limitations on the use of a DAF.  If the use is restricted to your organization alone, it doesn’t meet the statutory definition of a DAF, but you have to be careful to avoid inadvertently restricting your program.

Assuming that you can do it under applicable law, do you really want to?  Is the donor particularly qualified to assist with investments?  Is the fund part of a larger endowment or simply a fund to be expended in the near future? Will other donors want to be on the committee to mind their gifts? Will you keep their interest (and future gifts) if you disregard their advice?  There may be situations in which it makes sense to add a donor to the investment committee, but I would want to see very clear benefits before I would recommend it.