The best time to travel to Jordan is before or after the tourist season, i.e. May and early June and between late september and end of October unless you like  hot days. May ,September and October the tempretures is very pleasent and in the 70's. during that time you still could go to the dead sea, Petra and Aquaba. In July and August gets to be very hot and dry. however the nights are very pleasent in Amman during the summer months. People enjoy walking in the evening  and into the night during the summer months. No rain in the summer. The dead sea, Petera,Petra and Aquaba are wonderful in the winter time. the temperture is in the 70's and you will be able to swim in warm waters where Europe and most of the United States is very cold.

Jordan is very westernized when it comes to clothing. For the summer months business casual is best bet. for the evening if you are going to eat out , have drink and go dancing. No one wears shorts in public. Pants and short sleeve shirt  is the norm during the day unless you are on business then a suit is the norm.  You need a swimming outfit or two since most hotels have a swimming pool. also a light jacket is recommended. Same goes for women. For dinner parties and formal invitation women tend to be fashionable.