I'm also 5'2". I ride dressage, where it seems like giant warmbloods are the norm. I leased a taller horse ~16.2 or 16.3 before I bought, and was really glad I did. He was way too tall for me. I never felt like I was able to get my leg on in the right spot, I looked REALLY short in photos, and it was a long way to the ground when he bucked me off
I found that right around 15hh was the right size for me.
A lot of it's personal preference (especially gender and age), though, especially if you're just looking to hack around. There are a lot of smaller breeds that are a lot of fun to ride (Fjords, Haflingers, Pasos, etc.) that are perfectly suited to adult riders, and just because you're short doesn't mean you couldn't ride a bigger horse as long as you're comfortable with them.