I have never gone for 4 days, but I routinely go for 2 and have been pumping exclusively for awhile now. You have the right to carry your pump, breast milk, and ice packs with you on the plane. As the security explained to me, you don't even have to declare it verbally, unless they ask (having said that you may want to do it if you're anxious given some bad experiences from the answers below - having said that, I think it is outrageous and I wonder if those TSA people were in violation of their own rules - might want to check with them or their website in advance - I've NEVER had a problem and I travel almost every week). Keep in mind though that it'll be quite heavy and take up most of the space in your carry-on on the way back. I actually had good experiene checking my bag with all the milk, even on longer flights, but I certainly can't recommend that - it's a rik, no question.
Support all the advice regarding arranging with the hotel to have a working fridge in your room. Good hotels are very accommodating - I negotiate late check-outs as well, when necessary - explaining that I need to use the room to pump.
I would NOT freeze your milk for the road unless a) you are 100% sure it;ll stay completely frozen when you get home (and mind you - I had more than one airport delays in my experience - be prepared for those); b) you are going to feed it all in 24 hours upon return. Remember, you never re-freeze thawed milk, even it thaws just a little bit. From this perspective shipping on dry ice, if you can arrange it, might be a good idea. What worked for me was keeping it chilled in the fridge for as long as I could and then making sure I had plenty of ice with me to keep it cool in the mini-cooler. All of these should be easier this time of the year. BTW - from the handling perspective I personally always prefer bottles with good tight screw-on caps to even the best of milk storage bags.
Finally, from personal experience, be prepared for flight delays (as mentioned above) and for having to pump in a non-sanitary conditions in the airport. Please G-d you don't have to - it is one of the grossest experiences ever (and certainly dump that milk!), but you may need to do it to release the pressure and sustain your milk supply if caught on a long delay. From this perspective might be a good idea to have the pump and at least 2 empty bottles in your carry-on (even if you dared to check in your milk) and plenty of sanitizing wipes and hand sanitizer in your bag.
Good luck and don't worry, it'll work just fine. Just don't forget to pump every 3-4 hours regularly.