While there is an incredible variety of symbolism in Persona, as well as an incredible amount of symbolism just surrounding Mitsuru, I found the symbolism surrounding her element interesting enough to warrant an entire page in dedication.
The term "cold as ice" is largely used to describe people with distant or otherwise rough personalities that tend to come off as very mean or aggressive. "Stone Cold" is another term used to describe more rugged and aloof personalities. This term is often used to describe Mitsuru's personality upon first meeting her. She comes off very "cold", as she tends to be quite to the point and relies on logic, oftentimes disregarding people's emotions. Though she is later developed in a way that disregards her "cool" persona, first impressions almost always show her off as someone with a very cold demeanour.
In Tarot, ice symbolism often is used to describe isolation, patience, waiting, distance, and objection--all of which feed directly into her development, story, and social link. In Tarot readings, ice is used to convey a feeling of separation, as well as to tell of a season of deep contemplation--much like how winter thaws and turns into spring.
Another thing ice symbolizes is change. Ice melts during the warm seasons, much like how Mitsuru's personality "melts" and changes, showcasing just how warm and full of love she is. Her cold persona deteriorates, allowing the warm side of her to finally blossom. Her development is very similar to the changing of the seasons, from winter to spring. That's not to say she does a complete 180 in terms of who she is and how she acts--but the strength she showcases, as well as the strength she gets from her friends, helps her in learning how to show off more of the more sunny and bright parts of her, instead of always remaining very cold. Mitsuru is like a mixture of cold and warm, of spring and winter. While she still favours logic over emotion, she learns to take others' feelings and emotions into consideration instead of just going with whatever is most logical.
One of the biggest changes Mitsuru learns to make is to put her own well-being first, as well as learning how to express her own emotions. Ice represents that perfectly.