Disney is one of the biggest and most litigious entertainmeent companies on the planet. Please see this similar Q & As about a non-profit event involving Disney IP. You can research others here under "Research Legal Issues" under "Disney" to see all the Avvo posters who want to trade on Disney's IP.
PLEASE READ THIS BEFORE YOU COMMENT, EMAIL ME OR PHONE ME. I'm only licensed in CA. This answer doesn't make me your lawyer, and neither do follow-up comments and/or emails and/or phone calls, and you shouldn't expect me to respond to your further questions if you haven't hired me. We need an actual agreement confirmed in writing before any attorney-client relationship is formed. This answer doesn't constitute legal advice, and shouldn't be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.
Yes, they will have an issue with it. Unless you get permission from them, don't even think about it.
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.
Just because an organization or event is supposedly nonprofit, it does not get any special dispensations when it comes to the use of intellectual property. You might inquire what else is this group doing with the Disney theme. It is one thing if they buy and use authorized Disney merchandise, but they too could run into trouble if they are using unlicensed reproductions of Disney characters.
LEGAL DISCLAIMER: Please note that this comment does not constitute legal advice nor has an attorney-client relationship been created.The law may vary depending on the state in which you reside or the jurisdiction where the activity took place. This comment is intended only to give some direction in which to seek further guidance.