Coolers! I take a small, hard cooler (the size that holds a 6 pack of cans), put in some ice packs, and stick the LAs in there for the night. That way they are in easy reach.
If we travel, I pack all cold stuff in the cooler and we stay somewhere that has a fridge so I can freeze packs and keep everything in the fridge. Usually that first night in a hotel (after a day of traveling), I use an ice bucket with ice underneath the plastic bag with LAs on top of the plastic - because the ice packs haven't had enough time to freeze.
For nap time or when we go out during the day, I use a small soft sided lunch cooler with a small ice pack in it.