Frequency difference when water splashes at different temperatures

This is a guess since I have never done the experiment, but the viscosity of water falls by a factor of 5 on heating from 5°C to 100°C. The viscosity is one of the two factors (the other being density) that control the water flow, so it is quite reasonable to suppose that water at 100°C splashes in a noticably different way to water at 5°C.

I mentioned above that the density also affects the flow. However the density of water only changes by about 4% over this temperature range. So it seems likely that the change in the viscosity is the main factor.

My immediate guess is that it is because of the difference in viscosity due to temperature.

At 5 degrees celsius, water is around five times more viscous (dynamic viscosity ~ 1.5 mPa.s) than it is at 100 degrees celsius (dynamic viscosity ~ 0.3 mPa.s).

This means that when the cold water splashes, the droplets/jets will have less energy as viscous friction is absorbing some of the energy of impact. In the low-viscosity hot water, less of the energy from the fall is absorbed by viscous friction and so more is available to hit things and emit a higher frequency/ higher energy sound.

Other minor effects:

Surface tension is ~30% lower in the hot water (Surface tension and viscosity are parametrically related through temperature),

Density is 2.5% lower in the hot water

However, I just did an experiment with a mug of boiling water and a mug of chilled water and I've got to say I didn't notice the difference in the splashing sound. Maybe I need to do a more careful experiment.

Edit: did a more careful experiment and I noticed the slight change in pitch! Cool stuff! However I heard the change in pitch in the opposite direction to the one you describe, being slightly higher pitch for the hot water. My experiment was dropping water from either of two mugs (one boling water and one chilled) into a ceramic dish in the kitchen. Drop height of maybe 50cm, so probably shorter than your experiment.

There are a number of reasons:

The hot water has a lower density than cold water

Hot water will often be filled with tiny air bubbles, giving it a milky appearance. When cold water, with lots of dissolved air in it, is heated, its ability to hold dissolved air is reduced. The air is forced out of solution and into tiny bubbles.

But most important, hot water has a much lower viscosity than cold water. The viscosity of water at 70 degrees Celsius is about $\frac13$ the viscosity at 10 degrees Celsius. The hot water will flow more quickly through the pipes and splash differently when it hits a surface.

All of these will change the sort of sound the water makes in flowing through the pipes, and outside the pipes as well.