In pictures taken at the event, Lucas was looking so sweet as his mum cuddled him up in a blue puffer jacket that had animal ears on top.
Lucas' little face was just visible, as Zara had her son strapped to her chest – and he looks adorable.
Lucas is Zara and Mike's third child, and first son, as the couple are already doting parents to daughters Mia, aged seven, and Lena, aged two.
WATCH: Mike Tindall shares glimpse inside garden as daughters play
The mum-of-three wore a blue raincoat with jeans, a baseball cap and some sunglasses.
Zara was seen introducing Lucas to a fellow equestrian, before going on to lead some horses with the tot still strapped to her chest.
She later tucked him into his pram as the rest of the event unfolded.
Zara and husband Mike Tindall welcomed baby Lucas back in March, with Mike revealing that Zara had given birth on the bathroom floor!
A spokeswoman for the couple confirmed: "Zara and Mike Tindall are happy to announce the birth of their third child, Lucas Philip Tindall."
The baby was born at the couple's home in Gatcombe Park on Sunday 21 March, weighing 8lbs 4oz."
Zara looked besotted with her newborn. Credit: James Whatling + Kelvin Bruce
Mike spoke about the birth on his podcast, The Good, the Bad and the Rugby. "Sunday got even better because a little baby boy arrived at my house," he said. "Arrived very quickly. Didn't make it to hospital. On the bathroom floor. So yeah, it was running to the gym, get a mat, get into the bathroom, get the mat on the floor, towels down, brace, brace, brace."
The former rugby player revealed that Zara's friend Dolly, who was also present at the birth of their two daughters, recognised that they wouldn't have time to go to hospital.
"Fortunately the midwife who was going to meet us at the hospital wasn't that far away so she drove up just as we had assumed the posit (position) and the second midwife arrived just after the head had arrived," he added.
Zara was seen pushing Lucas around
Zara had already been seen with Lucas, when she attended the Cirencester Park International Horse Trials, although on that occasion she kept her son's face hidden.
On the outing, she was spotted chatting to other spectators as she pushed Lucas around the park in his pram.
Earlier this month, Mike spoke about having the "best day" with Lucas after Zara and their two daughters headed off together.
Zara and Mike are parents to daughter Mia and Lena
"A great Saturday, because Zara's horses were running so she went off to watch them, took the girls with her and I had the wee man, and literally you feed him, he goes to sleep, I went to the gym, he wakes up, I feed him," he explained on his podcast.
"I watched rugby whilst I was feeding him, he went back to sleep. It was the best day. Just the house on your own."
However, things took a turn when things changed the following day. "And then we did a role reversal the next day and I had the girls, and it was carnage," he said.
"Making, baking, taking Mia to rugby on Sunday. She's into it, she says she is not into it. 'I don't want to go, I never want to go,' and when she gets there, she always has fun so…it was a good family weekend."
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