Mosfet Conventional current flow direction in the circuit
MOSFET gates are very high impedance, so no current (or almost no current) flows into them in steady-state conditions.

During switching on/off there is indeed current flowing to/from the gate as it charges/discharges and reaches its required Vgs level. But this is only a transient condition. If your load is switched only from time to time, its steady-state condition is no current flowing to/from the MOSFET gate.

Additional suggestions:


If you plan to control inductive loads such as motors, use a flyback diode across the load terminals to avoid destroying the P-MOSFET due to inductive voltage spikes at its drain when the load is turned off.
Decouple the +12V supply rail with a big capacitor to avoid destroying the P-MOSFET due to inductive voltage spikes at its source when the load is turned off.
Due to the high currents involved, consider using an optocoupler instead of a BJT, to fully isolate the 12V circuit from the Arduino.
Consider using a logic-level N-MOSFET instead of a BJT for T1. If you decide to keep the BJT, then add a base resistor lo limit the current into the base. Also, add a pull-down resistor at the base to ensure the BJT is cut-off when the Arduino pin is at high impedance (something that can happen when the Arduino is off or when it is starting up, before the pin is configured as OUTPUT).