Duke and Duchess of Cambridge attend Ayrshire opening

The couple joined the Prince of Wales at Dumfries House in Ayrshire where Charles has led a regeneration project since 2007.

Hundreds of locals and 600 members of youth groups including the Girl Guides and Scouts turned out for the official opening of the Tamar Manoukin Outdoor Centre.

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

Kate, dressed in a red Armani coat and yellow tartan scarf, smiled as she was handed a “Princess Catherine” doll by one young well-wisher.

Royal fan Dayna Miller, 11, from nearby 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.”

Dayna’s 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 home 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 black tights, boots and gloves, was handed several posies and soft toys as she spoke to members of the public.

Charles remarked on the freezing conditions himself, telling the crowd “many people are probably about to pass out”.

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

“I told them I’m far too old,” he told the guests.

Dumfries House and its adjoining land were bought by a consortium led by Charles and which 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.

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.

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

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