Because Elsa had been cooped up for most of her life, she was basically cut off from any sort of interaction besides with her parents. She never got to go out and interact with anyone, especially around the time of puberty because that's mainly the point in time where people start to consider the attractiveness of others. Not only that, she was afraid to interact with anyone else because of her powers, so she never experienced what it's like to talk to anyone of the opposite sex (aside from the castle servants, but ya know...) or anyone outside of her family until her coronation. Because of this, I don't see her trying to be with anyone. I see her as asexual or at least would take her some time to catch up on what she had missed out on, and then maybe, just maybe find someone that she could be happy with (without worrying about accidentally freezing their heart)
And that's about it.
Queen Elsa © Disney
Stamp © me
IMO, I think Elsa is too traumatized and mentally damaged from the abuse she received from her so-called "loving parents", I think she would have too much emotional baggage to be in a romantic relationship.
Also, sometimes, emotionally and mentally damaged trauma survivors like Elsa don't need romance. It would make things worse for them than better.