Cooling trailer while towing

While I appreciate the ingenuity and creativity, this is an inefficient solution in search of a problem. Your Rv already has an AC that's pretty efficient at cooling without introducing moisture. It's cleaner and just easier. Get some power to it and use the solution you already have. Plug and play. Keep it simple. 

a real swamp cooler is the last thing you want to use on a rv because it introduce moisture to the rv.    I know you said that the ducting is enclosed so the ice just cools the outside of it, but cold metal and humid air is going to form condensation, if you have a drain then you can get rid of a chunk of it and actualy dehumidify the air a bit other wise it is just going to evaporate with the airflow again.  so in a sealed one ya it won't be as bad but it isn't as efficient as a open swamp cooler.  the cold plate idea is kinda neat, but you will get the same condensation forming so you have to figure out a way to handle that, and the peltier plates do take a surprising amount fo power for what you would want to do.  to give you an example the TEC1-12706 plate is a 12V peltier that consumes 6amps of power, constantly.  from this 72 watts you get 50 to 60 watts of cooling.  so that is between 140 and 200 BTU/hr so to equal the cooling preformance of a 15000btu AC, you would need about 80 of the plates, so that would consume 480 amps of 12V power.  we still haven't discussed how you get rid of the heat from the back side of the plate.  that has to be vented out somehow

there are 12V compressor rv's, but while they are more efficient than a 120V ac they still take some power to run, so you would be looking at batteries and enough solar, or running a generator while your driving, but it is a realistic option. 

the other thing I have seen laitly is smaller mini splits, but thats going to depend on the rv and where you can mount the outside unit.  

I don’t believe what you are seeking is possible. An A/C unit is simply a heat pump; it moves heat from one place to another. So in essence, you have to be able to pump the heat outside - you have to have a vent, there is no conceivable way around that. And while your putting a hole in the side for a vent, you can put one in the bottom for the drain also.

Your swamp cooler is basically a rudimentary heat pump. It”s moving the heat in the air vent tubing into the cooler full of now melting ice. 

Bags of ice?  
Idk much but how many Peltier chips would it take to cool a rv in the summer? And how many batteries/solar/etc?

Doesnt seem efficient to me at all.  
short of a huge battery bank and at least a 3k inverter, a generator is necessary.  No free lunches anywhere.  

Most people that want to cool their rv use a generator and the rooftop ac and turn it on about an hour before their destination. Never done it myself when we had our Fw, but I know people that have.