Thrall is a little younger than the Dark Portal, which is convenient since the timeline is usually described in years since the Dark Portal opened. According to the Chronicle, volume 2, he was born on Azeroth, in the year 1.
The best guess on WoWpedia is that the events of Before the Storm took place in the year 33, based on Anduin's age and that Kalec had become Aspect of Magic (which occurred at some point during the events of Cataclysm) five years before. There's nothing definitive about the passing of time in Battle for Azeroth; judging by previous timelines, the typical intent is that an expansion takes up about a year of in-game time, so it's probably still 33 during Safe Haven. Thus Thrall is about 32 years old, depending on when in the year he was born.
As for whether orcs naturally go gray in their 30s, well, that's another question. It would hardly be a surprise if his stressful time as warchief gave him premature gray hairs.