Unless you have stuff that you must keep frozen dry ice is probably overkill, and has the additional disadvantage that it's generally hard to find (in camping areas) so you can't replenish it if you need to.

Ordinary ice in a good cooler probably will last for three days if the stuff you put in with it is prechilled and if you don't leak air in/out of the cooler between gettin' a new beer out; and if necessary every grocery/quickshop/baitshop in the world has plain ol' ice if you need to top up.

Unless you're adding more fresh ice than will fit, it's a good idea not to drain the water from the melted ice, since it's probably as cold as you really need and what's really important is having enough "thermal mass" to keep the cooler cooled to "refrigerator temp" or close enough to it. The cool water left over after the ice melts has to absorb a whole bunch of heat to raise it's temp more than a little.

Do keep the cooler out of the sun.

As noted, dry ice can be dangerous since CO₂ is really sneaky and can cause all kinds of problems (like dead campers).

John