I'm afraid though that I won't be as attractive since majority of men prefer long hair (I'm a brunette btw). But I said "Why not!" and if I don't like it it'll grow back... can't be too scared to try new things.
Its hard to say with shorter hair, it really depends on your face shape/style.
For me, the shorter the hair the cuter the girl has to be haha. Like Emma Watson with her pixie cut [though you're not going that short], she's still epic cute, but the majority of girls probably couldn't pull it off.[But I'm admittedly kind of picky]
I think its cool you're willing to go for it though, its just hair in the end right?
Just remember that guys [people in general] preferences run the scale.
And to be honest I'm not sure if most guys prefer long hair, it just happens to be that most girls have long hair so there's more long haired girls with partners. For most, if you're cute/good looking, your hair isn't going to drastically change that impression.
I say go for it! I've had a bit of a pixie cut for the last 2/3 years and I'm growing my hair at the minute (seems to be taking forever! :P) and will hopefully have a cut like that too! It actually made me laugh when I saw the image as that's my ideal haircut that I'm aiming for too.
Like Bluemonk said, the majority of girls have long hair now so it "appears" as more desirable when really its just a distorted impression.
It does also depend on your face shape as to how short you can take your hair. After all, as long as it suits you and you look good with that style, your still going to be attractive so there's no reason why guys wouldn't like you.