Sacred Haven of Debauchery

No, I think if there are two ice cubes, then there are also two kinetic energies and two masses of the substance that need to be heated. And if we neglect lambda (heretics!), then we get:
2*mv^2/2 = 2*cmt

Which simplifies to:
v^2 = 2*ct
Therefore:
v = √(2ct), t=110, c=4200
v = 961 m/s

In my opinion, if they both evaporated, then the impact is completely inelastic. And the speed can be found by equating the two kinetic energies to the sum of the two heats required to heat the ice from -10°C to 0°C, the two heats of fusion, the two heats required to heat the water from 0°C to 100°C, and the two heats of vaporization. Then the mass and the twos on the left side will cancel out, and the speed can be found as the square root of what remains on the right side.

P.S. If the steam is also heated to more than 100°C, then the speed will of course be higher.