Throw as much ice at it as you can. Unless your outdoor temps are below freezing, I doubt you could over chill it with just ice. You also might want to read up on keg balancing and rethink that 2' hose. The co2 pressure required to maintain the c02 volume of the beer will dictate that you supply at least 9 psi of pressure. 9 psi of pressure coupled with the resistance of a 2' hose and you'll have a beer cannon
5' of 3/16" ID beer line is considered by most to be the bare minimum. Most people are happier with 7'-10'. Just coil up the rest inside the insulated box somewhere making sure it doesn't get kinked.