When you arrive at your Walt Disney World resort, you can leave your carry-on bags with Bell Services; we do this all the time! We often arrive from the cold, wintry North, so we leave our winter coats, long pants (hats, gloves, etc.) along with our carry-on items at Bell Services.
They'll be happy to give you claim ticket, with the number of items left with them, and you are free to roam the parks without the extra baggage. Upon your return, simply head to Bell Services, hand them your claim ticket and they'll be happy to help bring your belongings to your room.
Have a wonderful trip! Be sure to send any additional questions as you think of them! We love to help!