Woodman was a very kind, even-tempered stallion early in his career. Later in life, after going through EPM treatment and breeding a zillion mares a year, he got tougher. The worst Ashford stallion was actually Storm Bird, who required two handlers and a muzzle.
Caveats are said to be tough.
Honestly, though, much of a TB’s personality is due to handling. If you approach a Storm Cat going, “oh my god it’s a Storm Cat and it’s going to be difficult and spooky” then it probably will be. Like any other horse, firm, consistent handling will get you through many issues.