It isn't that big of a deal. You just develope skills to compensate for what isn't really a huge detriment to begin with. And it doesn't mean- it should never ever mean- that you stand in range and take punches.
Learn to accurately judge distance, something every fighter should do, and stay at the eedge of punching range. Make the other guy miss and counter. For an example...Google the Alberto Davila vs Kiko Bejines fight...I watched it last night so it is in my mind...Davila was 5'1" with short arms and outjabbing the fighter that not only had longer reach, but was taller as well.
That's the biggest thing- learning to control distance, and that has more to do with your brain than how long your arms are.