This has already been pretty well covered but I'll add in a few comments.
1. Compressed air will always, for practical purposes, be saturated when you take atmospheric air and compress it up 100 psig or higher and then allow it to cool down to ambient temperatures or close to it. You can see this with a copy of the steam tables and looking at the volumetric change as you compress that air.
2. I disagree with DLANDISSR in that if you cool air down to say 100F with CW, the bulk of the water will not drop out. Yes, using chilled water will definitely remove more water but air has progressively less and less capacity to hold moisture as it is cooled. By the time it is at 100F and 100 psig, less than 1% by volume of the air will be water vapor and the majority of the inlet water has condensed out unless you have very dry ambient air. At 40F, it's down to 1/6th or so of what it could hold at 100F. However, the air leaving the aftercooler in either case is still saturated so unless you chill it BELOW atmospheric temperature before distributing it, you will still have water condensing out in your distribution system as it cools off. For many industry air systems, that is why dessicant driers which can reach very low dewpoints (-40F at pressure or lower) are commonly used.
Basically, a cooler/receiver by itself will reduce the amount of water removed in your air lines but won't eliminate it. To supply dry air, you need to either install a chiller as DLANDISSR suggests or a packaged instrument air system. For 36F, unless you have chilled water available, a packaged PSA system would make sense. However, those usually want fairly cool inlet temperatures for the dessicant to work so you are back to a packaged cooler, receiver, drier system.
Find out who does compressed air packages in your area and talk to a couple of vendors to see what they suggest. Let them know what your budget is so they can concentrate on realistic options. If you are on a tight budget, I think your option is to install a small air cooler as you indicated with a receiver to remove the mositure that condenses at that point and then well trap your distribution headers to remove water as it condenses out along the line.