Don't worry, I've seen shorter people flying all sorts of aircraft. I can't think of any establishment, civil or military, that has its lower limit above 1,60 m - and you're not even close to that.
You didn't mention whether your idea was to fly a C172 for a hobby or progress any further, but it's not a concern in either case. The C172 has a good forward view as the glareshield is not exactly high. On the PA28 though, even some taller guys put a cushion on the seat because it has a relatively high glareshield in relation to the seat height. It's a matter of personal preference - and, if you are flying the aircraft privately, you have every right to pick up one which you find comfortable. Just like choosing your own car. If you want to progress onto something bigger and fly it for a living, it becomes even easier. Business jets and airliners alike have seats and rudder pedals which can be adjusted in a number of ways to accommodate for any body part proportions.