Natural AC, Stream Powered heat exchange
I know that seems like a cheap easy hack.  However it's not going to work very well, and to get it to work at all you'll have to pour some fairly serious capital into it.  

Given that, you would be better off using real heat pumping with freon.  But yes, use that creek water: it is an excellent heat-sink and will greatly increase the efficiency of the unit.  Heat pumps work best when they are pumping heat "downhill", i.e. the ultimate heat sink is colder than the space they are cooling.  

There are several sources for water-sourced heat pump equipment, but the most obvious is a marine air conditioner/heat pump.  They use seawater as their ultimate heat sink.   Seawater is very corrosive; your creek water can't be nearly as bad. 

Going with a proper heat pump instead of merely an air conditioner means you can set it for reverse mode, and get heat out of it also.  However that will stop working when ambient temp gets too cold.