I would though be paying extra for the airfare and less on Accommodation to go mid March - late June or in September. If Castles and 5* is your thing then there is no harm visiting in February. The Weather might be a bit chilly and the daylight hours on the short side but the scenery won't be closed.
1 Saudi Arabia is home to the worldâs largest continuous sand desert â the Rub Al-Khali, or Empty Quarter.  Oil was first struck in Saudi Arabia in March 1938, at a depth of 1,440 metres in the Dammam oilfield.
Profile of the Province. With its capital in Dammam, the Eastern Province is the largest province of Saudi Arabia that is located in the eastern part of the country. More than half of the province is occupied by the largest sand desert of Rub Al Khali (the Empty Quarter).