Opening gates from horseback can be tricky - the following sequence of photographs shows how it can be done.
Bring your horse parallel to the gate.
Take the reins in one hand, lean down and unlatch the gate.
If the gate opens away from you keep hold of the gate, push it open as you walk through using your leg to guide your horse around it.
When you are through the gate turn your horse around parallel to the gate, put the reins in one hand and reach down and shut it.
If the gate opens towards you give the aids for a rein back keeping hold of the gate and then use your leg to guide your horse's quarters.
Walk through being careful that it does not shut on your horse's quarters.