Why Anna Was Not Allowed outside Fact/Headcanon

We know that when the king ordered to have the castle gates closed and locked, Elsa was not allowed outside so that she could learn to control her magic properly, away from people.

At the same time, while Anna was not a danger to people, she was not allowed outside the gates, either. Why, you may ask?

Because the people of Arendelle would find that strange and suspicious, more so than keeping both girls inside all the time.

In other words, if Anna had gone out whenever she wanted, people would constantly ask questions on why she was allowed to leave the castle while Elsa never was. Of course, the king and queen would not have a good answer to this, and the people could have even started a riot on the royal family just to get answers.

So to save all of the potential troubles, especially for the equal safety of both of their daughters, the king and queen decided it was best if both girls were kept inside at all times.