The American leads a congested leaderboard at Royal Troon by one shot at four under par after a two-under round of 69 on Saturday.
A combination of strong winds and torrential rain made for conditions that world number one Scottie Scheffler described as the toughest he has ever faced on the back nine.
But Florida native Horschel thrived in the wet of the west coast of Scotland to edge towards a first ever major title.
"I've worked my entire life to be in this position," said the 37-year-old, who is a eight-time winner on the PGA Tour.
"I've been in the lead many times going into a final round. Obviously this is a major. It means a little bit more. We all know that. We know what this means to everyone.
"I know what it means to my legacy in the game of golf and what I want to do and accomplish.
"But I'm excited to be here. I've wanted to be here my entire life. I'm finally here. I'm embracing it."
Horschel revealed he will switch off ahead of a momentous round by watching darts thanks to his love of British sports.
The West Ham fan has sported the crest of the London club on his golf bag this week and has also embraced dealing with the rough conditions of links golf on the other side of the Atlantic.
"I get tired of golf where you're making full swings and you lean into a certain number and it stops," he added.
"I like when you have to be creative and find a way to get around the golf course, and I think I've always done that well for the most part.
"That's why I've always enjoyed days like this."
Horschel will play alongside South Africa's Thriston Lawrence in the final pairing from 1325GMT on Sunday.
