Imagine two very simplified scenarios: a world with waterfalls and one "without".
A system "without" waterfalls is ambiguous to say the least, but you could imagine a perfectly smooth, spherical earth, with no land features, so you have the same processes leading to water vapour and precipitation, but no rivers and waterfalls that lead to the formation of waterfalls.
In the first scenario, solar energy from the sun is used to evaporate water, some of which eventually precipitates much higher than sea level and eventually aggregates into a river which feeds a waterfall. Once the water undergoes a waterfall, you state there is some heating which I find entirely plausible. This heating, however, is some fraction of the kinetic energy resultant from the flowing river, which itself came from some fraction of the gravitational potential energy contained in the water raised above sea-level, which in turn came from solar energy.
So, some very small fraction of the solar energy eventually manifested as thermal energy after the waterfall (not to mention other losses leading to the waterfall itself, and the associated erosion and deposition processes before and after etc.).
In the second scenario, the solar energy still goes into the evaporation and precipitation of the water but you wouldn't see any contained in the waterfall itself (the kinetic energy associated with the movement of the water, deposition processes, erosion, etc.).
So where did the energy go? Assuming the precipitation occurred at the same altitude but the land itself had no mountains, hills, etc. with which to form rivers and waterfalls, then the rain itself must be distributing the energy back into the air via air resistance. That is, a rain-drop dropping further, or for more time, must be heating the air more than one that does not. Simply dropping it from higher up does not mean it hits the ground harder because I assume it reaches its terminal velocity relatively soon in its motion.
Therefore, in this very simplified description, the presence of the waterfall diverts some energy from heating the air into processes which heat (or move) the land instead.
It might be that some other effect, such as having rain droplets in the air for longer, causes some cooling of the air.
For me, the question basically comes down to: Do waterfalls divert more solar energy from direct heating than the same system without them, and my thinking is that they probably do - by a tiny, negligible amount.
Now, as said before, I imagine the energy content of these processes is totally negligible compared to other, more direct heating effects and would therefore not have any measurable effect on environmental temperature.
But, that said, I still enjoyed thinking about it, and would love to see other, more expert answers.