I was using my newly favorite spell Ice Storm on an unsuspecting goat, but I was disappointed when the visual effects of the spell wore out well before the spell reached the goat.

However, after a few more seconds the goat keeled over as if the spell had actually hit him.

Does this mean that the Ice Storm continues moving even after the visual effects wear out?

That might have been a minor graphical glitch, I use Ice Storm all the time and the range is pretty good. If you aim it properly it can hit a dragon while it's flying and slow it down just a bit. But I've never seen it "disappear" and keep hitting enemies.