weird. If it is hot enough to need my head soaking, the water will be at air temperature I would have thought
It depends on where your water comes from. The photo below was taken when myself and another cyclist were halfway up Mt Buffalo, in the Victorian Alps (this is a 900 metre climb, and moderately steep in parts). The maximum temperature at the bottom of the mountain was about 40°C and it was in the mid-30s at the top. Then we found this waterfall by the side of the road, and the water coming out of it was so blessedly cold!

I stuck my head under it, and it helped me remain cool for the next 5km or so of climbing. Of course, your average suburban drinking fountain wouldn't be like this, unfortunately, because they tend to heat up on really hot days.