The Saudi's maintain a token military that is sufficient to protect themselves for a short while and enough to allow them to participate in some regional conflicts. But they have problems with leadership and having enough soldiers to fill out their ranks. If you look across their country, there are more foreigners than Saudis working as most Saudi citizens live off their oil revenues.
In 1990, Iraq and Iran had recently concluded a very bloody conflict where they traded volleys of scud missiles, some even with chemical warheads. No one in the area wanted to mess with either Iraq or Iran in 1990.