Speech emotion recognition (SER) with audio-language models (ALMs) remains vulnerable to distribution shifts at test time, leading to performance degradation in out-of-domain scenarios. Test-time adaptation (TTA) provides a promising solution but often relies on gradient-based updates or prompt tuning, limiting flexibility and practicality. We propose Emo-TTA, a lightweight, training-free adaptation framework that incrementally updates class-conditional statistics via an Expectation-Maximization procedure for explicit test-time distribution estimation, using ALM predictions as priors. Emo-TTA operates on individual test samples without modifying model weights. Experiments on six out-of-domain SER benchmarks show consistent accuracy improvements over prior TTA baselines, demonstrating the effectiveness of statistical adaptation in aligning model predictions with evolving test distributions.