You could write a treatise on this one.  First, the IRS generally does not concern itself with whether or not funds are “restricted.”  This is normally a matter of state law.  Each state will have its own case law or statutes to support the concept.  You can find working definitions in the Financial Accounting Standards Board (“FASB”) materials such as its Standard No. 116 (now superseded) on accounting for contributions. These apply for financial accounting purposes, but generally reflect the state of the law.

Generally, funds are ‘restricted” when a donor places restrictions on their use.  Typically, there are two types of restrictions—permanent or temporary. 

Permanently restricted funds are those for which the donor says the recipient must retain the assets permanently but may spend only some or all of the income for specified purposes.  The Uniform Prudent Management of Institutional Funds Act, adopted in some form in all states except Pennsylvania as the successor to the Uniform Management of Institutional Funds Act, has separate rules for handling this type of funds, which it calls “endowment.”  (See Ready Reference Pages:  “UMIFA Sets Rules for Charitable Endowments” and “New UPMIFA Sets Rules for Management of Charitable Funds.”)

Temporarily restricted funds are those for which the donor says they must be used only for a specific purpose or after a certain period of time.  The income from permanently restricted funds will be considered temporarily restricted if the donor requires that it be used for certain purposes.  Your question implies that the funds solicited at the event will be temporarily restricted for a certain purpose.  (Subsequent to the original publication of this question, the accounting profession has essentially elliminated the distinction between permanent and temporary restrictions and lumps them together as "restricted."  The Form 990 also distinguishes only between restricted and unrestricted funds.)

The key to restriction is that it must be donor-placed.  Boards, acting alone, cannot normally create legally enforceable restrictions.  If, however, a charity solicits funds for a specific purpose, it is generally believed that gifts made for that purpose become restricted for that purpose because the donor, by contributing for the purpose, has adopted the restriction. UPMIFA specifically says that a restriction may be imposed by the manner of the solicitation.

Most charitable solicitation registration laws (and other state consumer protection laws) require a charity to use funds for the purpose for which they are solicited.  That is one reason why solicitations ought to include broad charitable use language as well as specific intent.  If you get more than you can use, or if the project changes, you can still use the funds for general charitable purposes.