[2.] Or maybe an open loop which takes water directly from the river.

I'd opt for 2 unless the area is prone to freezing - or even if it is, but only seasonally.  (You can empty out the lines before the freezin' season.)  Use a drinking-water safe plumbing.

1 Risks dumping antifreeze in the river if there's a leak - which can happen due to your underwater structure being hit by a rock or a boater or something.  So I'd only consider something like that if you're talking, say, a desert where it gets 'way hot in the day and may freeze the same night.  And then I'd still use drinking-water safe plumbing and a drinking-water-safe antifreeze (which could raise the cost significantly but would protect the river in case of leaks and thus you in case of environmentalists).

Such antifreezes don't have an anti-corrosion additive, and neither does river water.  So stick a sacrificial anode in the system (electrically connected to the copper and near it) where there must be copper, another buried next to the river and hooked to your metal if you put metal in the river, and use PVC or other plastic for getting to and from the river.  (Plastic is proably a good idea for the bulk of the runs anyhow to keep the water cool.)

A fan could push air through the radiator, thus cooling a room.

Do you have a forced-air furnace?  Put a radiator in it where you'd put the evaporator of an air-conditioner.  (You might consider using one of those for the job if your cooling load is light, or several if it's not.  They're intended for refrigerants that suck more heat so you may need more of 'em.)  Use a stock air-conditioner-controlling thermostat, but hook up your pump where the compressor relay would go.  All done.  B-)

If you pump water through your radiator at 10 gpm, and the water leaving the house is 10 deg F warmer than when it entered the house, you get about 48,000 BTU/hr.

Someone please check my math!

Air conditioners rated in "BTU's" are actually BTU/hr.  So you can compare this directly to the cooling capacity of an air conditioner unit.

The numbers above are linear with respect to delta T and flow rate, so if you have a higher or lower flow rate or delta T you can adjust the 48,000 BTU/hr number accordingly.

This is based on water weighing 8 lbs per gallon which isn't exactly right but it ought to be close enough.

You need a heat exchanger for the house designed to operate at a low delta T.  These can get pretty big (several coils thick).

Here's something I've wanted to try:

Find an old central air unit (only the part that goes outside).  All you neeed are the coils and the fan.  Get one that has coils that don't leak (maybe had a bad compressor).  HAVE A PROFESSIONAL RECLAIM THE REFRIGERANT.  Refrigerant molecules are so "slippery" (don't ask, this is what a chemist told me once) that they can leak from a hermetically sealed (air tight) container.  A unit that won't hold refrigerant might still hold water.  If you place the unit somewhere in the house and pump water through the coils the fan will circulate the air over the coils.  These fans are usually 240V, but you might be able to get a different fan.  You could even get a line voltage cooling thermostat (about $30) that will turn on the fan and pump.  Depending on the humidity where you live, you may need a drip pan under the unit with a way to get rid of the condensate.

It might be worth a try.

Car radiators are designed to shed a lot of BTU's per hr but they rely on a very high temperature difference.

If you find a source for cheap car radiators, get a few of them and stack them face-to-face and plumb them in series.

Blow your air through the "stack" in the opposite direction that the water is flowing.

You may still need a way to get rid of the condensate unless you live in a desert.

Good Luck,

By using your stream with very cool water, this would act exactly the same as a refridgerated air unit.  The temperature of the water will probably not be as cool as a refridgerated air unit, but will undoubtedly be able to cool enough to make your cabin very livable.  I suspect that you could cool your place off to be as cool as a refridgerated unit would but you may have to run the unit a bit longer is all.  

Stack the radiator so the cold water in is on the very last radiator the air touches , farthest from input, and run the water in series back through the radiators toward the radiator that the incoming air first touches, pretty self explanitory why.

 We have noticed for reasons I am completely clueless about. We did some monitoring and made a couple graphs, and the closer the air temps are to the river water temps the farther the exit water temp is from the air temps in house. so say river temp is 60 and house temp is 85 the exit water temp is 82 to 83,
 but if water is 65 the and house is 85 the exit water temp is 79 to 80,

It defies my grasp of logic ( which is known to be flawed A LOT.)
Can anyone fill me in on why ?

We have tried many ways to get the river to move the water but none have worked for us, this incline is way to much and river way to calm so we did a combo of rams, and electric pump , that way the pump doesnt need to be so large, and more efficient. Its probably worth experimenting combining ways to move the water. We gave up when it worked well but plan to keep trying someday in future

Oh yeah we used the water directly from the river , one less heat exhange and inefficiety to mess with.

Have fun keep us posted plz

When you can do all of this with a swamp cooler unit, save money, save time, gain efficiency, and gain a cooler home than using water inside metal radiators, then why use metal radiators?

Using them means water must first cool metal, which in turn cools air and in the meantime due to heat transfer the temperature raises again and the water must cool the metal down again.  This means the water has to work twice as hard to cool the air than if you were using a swamp cooler.  With a swamp cooler, the water only cools down the air.

Besides making the water work harder to accomplish the same task, adding radiators slows down heat transfer as well.  water (if given a good surface area) cools air more efficiently than metal does.  

Radiators is more expensive, and much more engineering since you will need to monitor your water flow to make sure that it is strong enough to keep the radiators cool enough to make a difference in the home (a task that sometimes proves easier said than done).  with a swamp cooler, all you need to do is make sure your pads are wet, your fan is pulling air through the pads, and your used water has a home to go to after it is used.  Your flow of water does not even need to be that strong.  Simple, deffinitely more effective, a fraction of the cost.

Devon

With 10 C = 40 F you can cool the house all depends on the water volume you use and the conversion method ( Fan speed etc).

Temperature closer to each other higher the water volume that is needed.

One needs the area & volume to be cooled to determine the litre/minute or gallon/minute of water to get the thermal transfer needed.

You will need many litre/minute to accomplish that ( you need about 40,000 btu/hour) which means a good water pump and a good radiator with a good fan or blower.

It will take much of my time, right now, to calculate what you need and since you are not set for it -- then we can leave it for later.