Sometimes she would ask her father how Anna was doing. There were days where she did not knock on her door, where she did not catch a glimpse of her when Elsa left her room. He would respond, giving her a quick summary of Anna's recent shenanigans.
After that, there was no further discussion. There was business that needed to be attended to. Ice powers or not, Elsa was still heir to the throne. She had to be prepared for when she took power.
It was a blessing to get to hear about Anna, to learn that her sister was alive and well. Elsa could not check on her herself, but at least others could.
Still, she couldn't help but miss her. All she wanted was to be able to open up that door, to let Anna in. Yes, she wanted to build a snowman! She wanted to ride her bike around the hall, to play pirates and knights with Anna.
But she couldn't, and for good reason. There was no way that she would ever be able to play with Anna without risking hurting her again. Years later, she still had nightmares about the night where she hurt her sister.
Still, that couldn't stop her from wishing.
There was another wish she had, another wish that she knew that she could say aloud. If she couldn't play with Anna, then she wished that one of her parents or a servant would. They were the lucky ones, free of powers. They probably didn't even realize how lucky that they were. But instead they ignored her, leaving her to wonder. Usually she ended up back at Elsa's door.
"Do you want to build a snowman?"
Elsa would nod, though afterwards she would usually tell Anna to leave her alone.
Elsa never would build a snowman for herself; using her powers for fun had been dangerous. Her gloves were better, a way to stop her powers.
As long as she had those, Anna could at least think that Elsa was normal too.