The Duchess of Cambridge was impressed with a doll that a young girl thought bore a remarkable likeness to her as she visited Ayrshire.

The pregnant royal braved the cold as she joined the Duke of Cambridge at the opening of an outdoor centre at Dumfries House near Cumnock.

There they met the Prince of Wales on the second day of their trip to Scotland, having visited Glasgow on Thursday.

Royal fan Dayna Miller, 11, from Coylton, showed Kate the doll which she got as a Christmas gift from her mother.

The youngster said: "She looked at it and she said, 'Does my hair look like that?'.

"Then she asked me where I got it from."

She added: "Kate's much prettier than the doll."

Her mother Sharon, 48, who wore a crown to meet the royals, said she bought the doll online for her daughter.

Gwen McLelland, 68, lives near the 18th-century Dumfries House and took her nine-year-old granddaughter Eve Park along to see the royals.

She said: "The Duchess thanked us for coming out in the cold and we told her it was worth it."

Kate, who wore a red Armani coat, was handed several posies and soft toys as she spoke to the public.

She is known as the Countess of Strathearn. The Duke is the Earl in Scotland.

Charles, who is the Duke of Rothesay in Scotland, remarked on the freezing conditions himself, telling the crowd "many people are probably about to pass out".

As Charles prepared to address the crowd, William rubbed his cold hands and told his father to "make it brief".

Charles said he was "enormously grateful" to the Manoukian Foundation for funding the outdoor centre and its 10-obstacle assault course, but said he would not be attempting the course himself.

"I told them I'm far too old," he explained to the guests.

Dumfries House and its adjoining land were bought by a consortium led by Charles and has overseen major renovation work in the last six years.

The outdoor centre is the latest addition and houses up to 52 young people.

Members of the youth services already have the venue booked every weekend until December.

Local young people have access to the centre during the week.

Among the groups at the event were the Boys' and Girls' Brigade and the Sea, Army and Air Cadets.

The Prince created the umbrella organisation Youth United in 2009 in a bid to promote the young people's associations.

Youth United chief executive Rod Jarman said it aimed to make at least one of the groups available to every young person in the UK, with a particular focus on deprived areas.

Northern Scotland's most senior sea cadet, Hannah Strachan from Peterhead, in Aberdeenshire, met Charles and William, who asked the 17-year-old about her time with the cadets.

"They were really friendly," she said.

"I think it's great they came today, it shows that they know we are here."

The visit ended with a flypast by two Typhoons of 6 squadron RAF Leuchars – the base near St Andrews where Kate and William met as university students.

The visit to Dumfries House was William and Kate's first joint engagement only with Charles.

The Cambridges have joined the Prince before for official events but Camilla has been present.

Stephen Kay, head of education and training at Dumfries House, said the assault course was designed to test critical thinking, problem solving, and to encourage people to work as a team.

The estate already boasts an art studio and a hospitality training centre.

Mr Kay said: "It's all part of the Prince's vision of getting people out and into activities.

"To have him and the Duke and Duchess here today has been great.

"The young people have got the chance to see there's a lot of interest in what we're doing here."

The couple later visited Barrow-in-Furness, Cumbria, where they met the naval crew of Astute Class nuclear submarine Artful.

A Clarence House spokeswoman confirmed the royal trio's visit was a first and described exactly how the historic visit came about.

She said: "The Prince invited the Duke and Duchess to look at Dumfries House and to look at the other projects."