Kathryn Beaumont, who had provided the voice for Alice in the 1951 motion picture, was brought back in 1982 to record narration tracks during the rehab of the attraction.
Originally Alice In Wonderland was planned to be a walk-thru attraction.
Voices:
Alice - Kathryn Beaumont
White Rabbit - Corey Burton
TweedleDum & TweedleDee - Corey Burton
Cards - Corey Burton
Cheshire Cat and King of Hearts - Tony Pope
Complete video of Disneyland's Alice In Wonderland available at DLDHistory.com