Hi there Kasey,
You are going to have a magical time while visiting The Happiest Place on Earth. Thank you for writing us here at the Disney Parks Moms Panel with your question.
The Disneyland Resort has thought of everything to make Guests experience magical. When my littles were young, I utilized the Baby Care Centers often to nurse or change a diaper. The rooms are quiet, air-conditioned, and sanitary. So if you want to go there to pump to keep your milk supply up, I highly recommend it. The Disneyland Resort does not offer cold storage options, however they do offer lockers for storage of small items for a small fee. You could bring an insulated pack or small ice chest to put in the locker and then store your pumped milk as the day goes on. Here is some more info on the
Baby Care Centers. At Disneyland Park, lockers are available outside the Main Entrance and on Main Street, U.S.A. Over at Disney California Adventure Park, lockers are located at the Main Entrance and the Golden Gateway.
The lockers are there for Guests to store things such as coats, bags, or magical gifts they have purchased that they do not wish to carry throughout the day in the Disneyland Resort. The locker rentals are $7, $10, $11, $12, or $15 per day, depending on the locker's size. Lockers provide unlimited access throughout the day.
I hope this helps and that you have a pixie-dusted visit. If you have any more questions, please visit me here at the Disney Parks Moms Panel and let me know how I can help you plan your magical vacation.
Wishing you magic!
~ Lynette