7 segment LEDs on wood face
This is done by carefully placing a layer of wood veneer over the 7-segment displays. The veneer is thin enough to let the light pass through. I wouldn't be surprised if some manufacturers use brighter than normal LEDs to make the display easier to see. Here is a video detailing an example.

It is also possible to simply drill out the wood to make it very thin where the 7-segment displays go. Here is an example of drilling the solid wood to be very thin.