At what resistance do I not see a voltage drop across a resistor?
If your voltmeter is digital, it has a least significant digit that will read zero until you overcome that threshold.  It also has a finite input resistance, for example say 10 megOhms.

So it's a simple voltage divider problem.  The meter resistance/(wood or whatever resistance + the meter resistance) has to be greater than one least significant digit to cause the meter to read anything.