Your hands usually become stronger and more flexible as you play more. I dont really have big hands, in proportion to the rest of me. I guess they are big compared to the guitar though, because I'm a big person (I stand about 6 foot 2 and a half)
My hands did become more flexible as I played more. I used to have trouble reaching the 5th fret with my pinky, now I can to fancy pull off and tapping tricks from the 6th fret using my pinky( major streaching).
My advice to you, make up some streatching excersises and practice them often, they'll help you bigtime.