These come up for sale from time to time:
https://olive-drab.com/idphoto/id_photos_m149.php
Buy one here:
http://www.vintagemilitarytrucks.com/Military_Water_Buffalo_Trailer.htm
Not cheap, but you’ll will it to your grandchildren if you take care of it!!! 
No price on this but it gives you some ideas of design:
https://www.machinerytrader.com/listings/construction-attachment/for-sale/24541211/2018-circle-d-truck-sales-300
You might find some used with Google’s help.
Here’s a source for tanks of various sizes:
https://www.ntotank.com/detailing-tanks
You can put one of these on a trailer and fill it with a pump along the water source and then use your tractor to move it and wet down the arena.
The only major difficulty with moving water is that it weighs 8 lbs/gal (more or less) and that means you need a robust unit to haul more that a few gallons. Stuff that comes from the Army is usually made to be “soldier proof” and that means it’s ROBUST! 
Pumping water 400 feet (likely uphill) is going to take some power particularly if the pipe is bigger than a garden hose. You’ll have to do a “yellow pad comparison” to cost out the delta between a transport system and a pumping system. In doing that, consider the cost of labor. If you make your 400’ run permanent then you have a one time expense. If it’s not then do you have to take it up and put it down whenever you use it? If so, that’s a big labor cost. If you leave it down on the surface what’s near it to damage it and require repair/replacement?
Could you do a standpipe? Put your tank a few feet off the ground to get some “head pressure.” Than put a pump on the tank to move the water to the spray heads. Fill the tank by submerging a “sling pump” in the river that will use the force of the current to pump water into the tank. This would mean that you require no energy to fill the tank and not all that much to actually spray arena. Here’s a company that makes sling/ram pumps. There are a bunch of DIY videos on utube.
Good luck in your program.
G.