Not sure have materials now improved ?
materials have changed massively since the original planks of wood...
As I understand, ski technology/design was pretty stagnant for years and years, then snowboarding came along and they developed side-cut, profile shapes and manufacturing techniques, etc. and that rippled back into skiing.
I'm a snowboarder at heart, been teaching it for years, and built my own board in the past - so have a slight idea about that construction and believe skis are similar.
I seem to remember a board is constructed as:
top sheet - plastic sheet with printed graphics
fibreglass mat
wooden core - type of wood (think Poplar is popular), grain-direction and number of pieces depending on cost and flex.
fibreglass mat
Plastic sheet on the bottom (sintered for high-end and extruded for cheaper)
The wooden core is surrounded by a metal edge and there's a vibration-dampening material (sometimes cork) wrapped around the edging too. To add extra "spring" to the board/ski you can get strips of carbon fibre tape on this wooden core, with the placement and direction all down to what flex and characteristics you want.
This is all squeezed and heated together in a press to provide the camber/rocker/hybrid/etc. profile shape. The excess resin is then cut away to follow the metal edging, and thus you have a board/ski.
Some companies have done v weird/creative things with the materials in the past. There was a German company (the name is on the tip of my tongue and it's annoying me, think it begins with a "S") that came up with a weave-layup that basically adjusted the flatness across the board as it flexed along the length. As you carved its edges actually dug down into the snow and gripped more, but if you bent it the other way (such as boardsliding a rail) the edges lifted up, like a boat hull (or Battaleon's TBT). Crazy tech.
Full carbon would be v v v stiff and thus it probably wouldn't be fun or forgiving to bumps/chatter.