We study the influence of dielectric function of metals on the transmission properties of terahertz pulses through periodically patterned subwavelength holes. Because of a drastic increase in the value of dielectric constants, most metals become highly conductive at terahertz frequencies. Extraordinary terahertz transmission is observed in subwavelength hole arrays made from both good and poor electrical conductors. The measured transmittance of terahertz pulses is found to be enhanced with increasing ratio of the real to the imaginary dielectric constant of the constituent metals, for which the dielectric function follows the Drude model.