Their trip also includes a visit to a medical institute to meet academics and discuss Sweden's approach to managing mental health challenges, a subject the royals have campaigned about.
With the clothes and the castles and the crowns, it's often hard to identify with royals.
Later in the day William and Kate met with Sweden's King and Queen, Crown Princess Victoria and Prince Daniel before going on a walkabout with the Crown Princesses and Prince.
Prince George's parents also got to try some warm, non-alcoholic glögg as they sipped from a flask to combat the cold (below).
Post-lunch, the royals took to the streets of Stockholm to walk from the Royal Palace to the Nobel Museum.
"Kate had played field hockey and I was expecting her to be good, and she was very good ... she had a very good swing", Anna Widing told media.More news: Spy vs. Spy - "Cozy Bear" election hackers undone by hackable security camera
William and Kate began the evening with a short meeting with Sweden's Prime Minister Stefan Lofven and his wife Ulla, describing their visit to the host country thus far.
While looking at numerous exhibitions, Kate got the chance to try out one designer's chair. "The category we help most is teenage girls and they prefer swishy wigs at the moment", said Monica Glass, manager of Little Princess Trust.
Kate is pregnant with the couple's third child, and despite an intense bout of morning sickness earlier in the pregnancy, she's expected to be a part of all the events on this royal tour.
The Duke and Duchess of Cambridge don't think it's fair to the other patients at the hospital or their families.
No stranger to royal tours, Kate has become the master of mixing home-grown British brands with local labels and designers and always dressing impeccably for the occasion - whethere it's a state function or a casual meet-and-greet. They will be leaving Prince George and Princess Charlotte behind.
Kate and William will then head back to the Royal Palace for a dinner in their honour.