The charity provides riding and carriage driving to over 28,000 UK children and adults living with disabilities every year, for therapy purposes, achievement and fun.
Anne told the ITV doco: "One of the things my father said was, 'You'll be offered a whole lot of things and the big mistake that was made in the past was just accepting anything that anybody asked you to do'."
"And he said, just be a bit careful and find something that either you're interested in or something where you might be able to have an impact."
For Anne, that was the Riding for the Disabled Association, admitting she had "no knowledge of disabilities, but some knowledge of ponies".
She's now been part of the organisation for 50 years and plays an active role in shaping its future.
But it seems she hasn't managed to say "no" to everything, as she's president or patron of around 300 other charities.
In 2010 the Princess Royal said she'd "pretty much stopped taking anything on".
"Only every time I say that someone or other, the Queen or perhaps my father say 'perhaps it's time you cut down but, by the way, we need you to do this'.
"It's not as easy as you'd like it to be ‒ it's quite difficult to give things up."
Riding for the Disabled's Sarah Heynen said Anne was "incredibly inspirational" for everyone involved in the organisation.
And its chief executive Ed Bracher said they were "extremely fortunate" to have her as their president.
"She absolutely believes in what we do."
Anne has been patron of the charity since 1971 and president since 1985.
