I have my CCW, I have been pulled over while driving out of state, and was required to provide my CCW info. In my experience there was no grief given by the officer, infact he was quite professional about the whole situation. Granted, every encounter with LE is different, but I have never had an issue with it. It is, however, very important to do your research on where you plan to travel. Is CCW even allowed there? Does the state you're visiting have reciprocity with your states CCW laws? And are you carrying in conjunction with their state laws?
Here is a great link for you with the basic info regarding reciprocity, then you will want to check the individual state's laws further regarding How to carry in that state legally.
Welcome to the club
(FYI, Utah honors NY permits, NY does NOT honor Utah permits. This has to do with class requirements. NY's class satisfies Utah's requirements, while Utah class does not satisfy the requirements of NY's permit laws. It's confusing I know....)