Dust in the atmosphere (if enough) can be very serious. Because of Krakatoa, the temperature around the world dropped 3 degrees lower than normal for about 2 years.
Though, from the size of the impact of Lavos, I'd doubt that that much dust would have truely caused the ice age. The reason why the K-T meteor was so effective was because the blast sent shockwaves and a dust cloud and kinetic wave away from the crator, which made more dust go into the air, and also that same blast wave killed even more dinosaurs.
Because no one in Ioka was hurt, or there was no dust cloud over the city etc, and even Crono and co didn't get covered in dust, then obviously it didn't happen to that degree. Since the Reptites Castle was pushed underground, the land it was on may have been evaporated, by the castle obviously withstood the pressure.
Also, I always got the impression that Lavos' appearance and his "going fast into the earth" ment that he was already inside it, gathering energy. That would also explain the reason why the Iokan decided to say that "there is no more sweet water". Why isn't there? Because if the sweet water revives strength and stuff, and Lavos is stealing that strength from the planet, then the planet surely can't let any more of that sweet water continue flowing.