In my opinion, Arthur Weasley seems like a person who overcomes his fears and calmly does the job that needs to be done. In Book 4, when the Death Eaters were terrorizing everyone at the campsite of the World Cup, Arthur was calm in the face of danger and ready to fight. (page 120) Also, he was calm and determined at the Battle of Hogwarts in Book 7, and other people must have seen duelling skills and leadership in him because he was put in charge of taking groups onto the grounds to fight. (page 611)
However, Arthur wasn't calm when he was afraid George was hurt in Book 7 - he was kind of fierce. Remember how he yelled at Kingsley even though Kingsley probably had a wand pointed at him?
page 74 American edition - "I'll prove who I am, Kingsley, after I've seen my son, now back off if you know what's good for you!"
Harry had never heard Mr. Weasley shout like that before.
The only time I can recall Arthur getting nervous is when he is trying to avoid confrontation with Molly. He has a healthy respect for her wrath! But remember, it was Molly who was falling apart after the World Cup incident and Arthur who was soothing her in Book 4. (page 146)