No I'm the same height and have ridden a 13H pony, it just depends on your weight. Height has a affect up to a certain point it's just the weight you really have to watch.
Not at all! Especially if its a rounder/chunky pony that accommodates more leg haha. I'm 5ft and have a 13hh pony and we work well together!
Nope! I'm 5'4" and ride 13.2 and 14hh ponies.
If is a wider pony and a lighter rider I think that would be okay. I'm 5.6 5.7 and my horse is 15.3 and it's the perfect fit. Have you looked into medium sized horses? Or are you just set on ponies?
It all depends on proportions - take some pictures and ask yourself things like:
Do I look silly? How close are my heels to going past the barrel?
depends on pony's build and yours. i am 5'2 and can still ride the 12 hand ponies