How easy is it to expand a door's rough opening?
The question describes this as a cosmetic change rather than a necessity, and it's in an exterior wall. It will be a structural change and a serious expense to expand the opening.  It will be much less expensive to find a door for your existing opening, or even get a custom door or modify a door. 

Expanding the opening would not be a handyman job. You would need to provide plans, get a permit, and have it inspected (and it isn't the kind of work where you should think about bypassing that process; doing it improperly could have serious consequences, your insurance company wouldn't cover it, and it could jeopardize selling the house in the future). Have a general contractor give you a price if you're curious.

There are still options for dealing with the door.  


Widen your search for a standard door you like.
The manufacturer may be willing (for a cost), to make a door you like in a narrower size.  
A solid wood door that you like in the next larger size can sometimes be trimmed on the sides enough to fit the smaller opening.  If the rough opening is nice and square, it may be possible to make a slightly wider custom door frame that would reduce how much needs to be trimmed from a wider standard door.  
A door can also be custom made from scratch to whatever exact size you need.  


These options would be more expensive than a stock door, but they will still be much cheaper than widening the rough opening.