Here is a quick weather chart to help you with planning your Arabian trip at the initial stage:
Dubai and Oman are great places to flee with us during the winter. The best time to visit the Arabian Peninsula, in general, is between October and March, when the weather is pleasant and cool and one can enjoy being outdoors.
From April on it already starts to get really hot and sightseeing might be difficult because of the heat.
We would highly recommend not to travel to the region between May to September, when the weather will be scorching hot, except for Salalah in the South of Oman, which has a moderate climate during these months. The rest of the region will be unbearably arid and dry.