I don't think anyone answered your question, you can still order and I'm sure you probably already did, but incase you didn't, get your order in as soon as you can. They ususally post dates that are closed once they start getting to many orders for certain days, as the days get closer to the time your about to be there you'll see that on the site. Might want to check and see if that's the case, I doubt it since it's the time of the year it is.
You don't have to order to far in advance, but about two to three weeks just keeps you safe.
As for the original poster, we took our own cooler with us to keep the milk cold. I took a soft sided cooler, that you can pull. It was the best idea I came up with, with all the exspenses of the trip my dh was putting his foot down about anything else being bought. So I folded it flat and put it in the bottom of my sons suitcase, once there we filled it with ice every morning and every evening before we went to bed, worked like a charm! The rolling thing was genius! I would have my son take out the milk and sodas, water bottles and put them in the sink (btw, if you have two sinks you can use one for the milk and fill it with ice) then he would take the cooler outside and dump the water and then roll it down to the ice machine and filler up! He would roll it back and then put everything inside and off we would go to the park, when we would come back, everything was right as rain!
I do think they have styro foam coolers to buy at garden grocers, this is an add exspense, but if you don't care, then that would be a good way to do things also.
Have an amazing and magical time on your trip!