Avoiding snow melting with salt
This article and this article (posted by @Jun-Goo Kwak in the comments above) say that the salt was used to lower the melting point of the snow on the surface, which would cause it melt. It would then re-freeze (I am assuming either at night or due to being in contact with snow beneath it), forming an icy layer on the surface. I don't know anything about Alpine skiing, but it seems that an icy surface is better than a slushy surface.

The ice would also form an insulating layer on the surface, which might help keep more snow from melting. Ice is a better conductor of heat than snow is (snow contains a lot of air, which is a terrible thermal conductor), so it is unlikely that it would act as an effective conductive insulator. However, it would shield the sub-surface snow from convective heat transfer caused by the movement of air. This is how igloos and snow caves work.

There could also be an effect due to the phase transition of melting - when ice melts, it is an endothermic transition, which means it absorbs heat. Some of that heat comes from the air, but some of it will also come from the snow directly below the surface. The result could be that the snow melts more slowly than it would if it were not covered by a layer of ice. The reverse of this effect is the reason that spraying an orange crop with water right before a hard freeze can save the crop (pg. 3) - as the water freezes, it releases heat (freezing is exothermic) and some of that heat goes into the orange trees. 

It is hard to guess which effect is most important (insulation vs. endothermic heat transfer), but I would say that both should be considered.

So, to answer your question, in both cases the idea is to melt snow and/or ice, but in the case of roads, we want the ice to melt immediately and flow away, so we use lots of salt. In the case of Alpine ski events, we want a little snow to melt and then re-freeze, so we use a little salt.