Does adding ice to sparkling mineral water extend the 'fizziness' of the solution before the drink goes flat?
Let me lightly gloss over the issue of nucleation sites and ice. While one observes bubbles forming on ice in the glass, they continue to form on the glass as well.

Instead, one could well ask the impact of temperature on release of the carbon dioxide, and thermodynamically that does come down to the solubility of carbon dioxide in water. Since this is of great importance to the soda industry, the study goes back some ways. R. Wieb and V.L. Gaddy, "The solubility of carbon dioxide in water at various temperatures from 12 to 40 degress and at pressures to 500 atmospheres - Critical phenomena', Journal of the American Chemical Society 62 815-817 (1940) shows measured solubility curves close to the temperatures of interest. One should note the increase in solubility as the temperature is dropped from room temperature down towards zero C.

While the carbon dioxide is supersaturated in the soda water, the driving force relates to the difference of the supersaturation to the solubility limit. As the temperature decreases, the thermodynamics favor retention of more carbon dioxide, which will then come out in your (warmer) mouth, giving you that 'fizz'.

Further, ignoring nucleation sites on the ice being much better than on the glass, as the temperature is decreased, the kinetics of nucleation will be at least partially suppressed as well.

Plus, I like my soda (and beer) cold, not warm!