If she gets trapped in the ice, she could exhale from her nostrils to melt the ice in front of her face. As Cisco pointed out, Katara in the series finale completely covered herself in ice and was able to melt the bit in front of her by exhaling. Iroh could also exhale steam from his nostrils that was hot enough to make metal red-hot, so it's been shown that firebenders can do this too. If I recall, a relatively untrained Zuko in the first episode also exhaled steam. The reason why she didn't do this in the finale is because Azula had gone craycray by that point. With one good breath, Azula can create lightning that is capable of
shattering rock, so it should let her smash through the ice. As seen with Mako, firebenders can still make lightning with very little
movement.