This is a question that should be resigned to the history books. However, I must get a message or a comment on this subject EVER DAY.
So, here are my thoughts.
1. We've all seen kids playing guitar really well on youtube, on video or in person. If hand size alone was really the issue then this simply wouldn't be possible.
2. It is a fact that many legendary guitarists such as Jimi Hendrix or Chuck Berry had larger than average hands. However, many amazing guitarists such as Angus Young from AC/DC have smaller than average hands (he's only 1.75 metres tall!) Prince was also such an an amazing guitar player, but he was smaller than average in height and could be said to have small hands.
Does hand size matter?
Yes, having a smaller than average hand size does make some chord grips tougher. For example, the C major chord was a real issue for me when i was first learning, and it can give many people trouble.
However, if you're hands are massive or on the thicker size, then it can be hard to even play what I consider to be the two easiest chords on guitar - E major and A major.
However, there are always ways around this.
The 1 finger E & A chords come in very handy for those with large or small than average fingers, for example.
Would a smaller guitar help?
Sure does. My first acoustic guitar was a Crafter 550fx. It has a super slim neck and a slimmer body, which made it much easier to play than other guitars I tried out as a 12 year old.
My Faith Nomad 'travel size' guitar is another good example of a great guitar for those with smaller hands or smaller body size.
However, the real trick is to find what it is that works for you and double down on it.
Whenever you learn and chord, a scale or even a song, think to yourself, 'is there an easier way for ME to play this?'
For example, I have NEVER got on with this way of playing a barre chord.
I've always preferred playing this with fingers 2 3 and 4 in a line.
You HAVE to take things like this into account.
And of course, through experience, the more you play, the easier spotting what works and finding alternatives for things that don't become.
Finally, let me leave you with this.
If you REALLY believe that your hands are just in no state to play guitar, then watch the video below. Then, consider whether this is something that you really want to do or not. Because if you do, then nothing, NOTHING should stop you from progressing and making music on guitar!