Repetition is the key - if you're in a new situation you're going to find it more intense. I know when a family member smashed up their ankle with a simple fall (from a slip anyone could have had on a wet day) it showed me how precious mobility is and how that could have happened to anyone... not to mention the weeks if not months if healing, physio and rehab it takes once something happens to you.
Personally I don't have an issue with heights but that is mainly as I'm practiced at moving over rough terrain - however I still take my time regardless of weather conditions. Same with abeilling, once I had a 'near miss' I was a lot more careful with checking and double checking, taking my time and having the focus entirely on the task at hand rather than worrying about it. Overall I'd much rather be out and about even being a little pensive, than not choose the routes with exposure at all...