The Mad Tea Party - or Tea Cups as they are more commonly referred to - were an opening day attraction at Disneyland. That's primarily because they were really an off the shelf carnival ride, gussied up a bit so that the ride cars looked like teacups rather than just an ordinary round car.
This postcard is from a very early series of Disneyland postcards. In fact, according to Disneyland the Nickel Tour by Bruce Gordon and David Mumford, it is from the second series of postcards to be sold! The first series featured mostly concept art of the yet-to-be-built park, and this is from the first series to sport actual photographs of Disneyland it all its glory.
By the way, if you don't have a copy of Disneyland the Nickel Tour, and you are in any way interested in Disneyland or Disneyland postcards, it is a must. It can be a little hard to find, and these days it is also a little pricey, but an invaluable book.