Like the IRF520N, data sheet says Gate Threshold Voltage being 2-4V @ 250μA, max being +/-20V.
The gate threshold is not the voltage when the FET is on. It is the voltage where the FET just starts to begin to turn on. The FET still has a high resistance at the gate threshold, it is not until the full gate voltage is applied that the FET is fully on. Any voltage between the gate threshold and the full on level puts the FET in the linear range where it is in effect only partially conducting. Thus it will have some voltage across it as well as current down it. Basically it will get as hot as hell very quickly if it is conducting any significant amount of current.
The figure to look at is the drain source resistance, this is given at a specific gate voltage. You must apply at least that voltage to fully turn on the FET. Voltages above this value normally do not decrease the drain source resistance to any great extent, if at all.