Nope, Walt Disney did not have any part of himself put into cryonic suspension before or after his death.
And contrary to urban legends, his corpse definitely isn't stored under the Pirates of the Caribbean ride at Disneyland.
He died in 1966, was cremated, and was buried at Forest Lawn Memorial Park in Glendale, California. You can go visit his grave there and find out for yourself. At that time, cryogenics was at its infancy as well.