Ice buildup on wind turbine blades is a significant issue, leading to operational risks and reduced efficiency. Conventional ice detection methods, such as visual inspection, power curve analysis or specialised sensors, are often slow, inefficient, or costly. This paper proposes an approach using 0-dimensional persistence homology from topological data analysis (TDA) applied to tower and blade vibration spectra. This method extracts key features representing the lifespan of the sub-level sets of the spectra, allowing the formulation of a clearer supervised learning problem. The resulting persistence diagrams are embedded into persistence images and persistence rank functions. Persistence images are employed alongside convolutional neural networks (CNN) to distinguish asymmetrical ice distribution on one or two blades as well as symmetrical ice distribution across three blades from normal conditions. For the symmetrical ice distribution scenario, persistence rank functions with functional principal component analysis (FPCA) and support vector machines (SVM) offer a simpler classification. This approach not only improves ice detection accuracy but also reduces equipment costs and maintenance, promising enhanced wind turbine blade monitoring and maintenance efficiency. Note to Practitioners-This study is motivated by the need for an accurate ice detection strategy in wind turbine blades that ensures precise and reliable detection. It utilises standard data from wind turbine structural vibrations to avoid additional expenses associated with specialised sensors. Unlike traditional faults, the gradual accumulation of ice on wind turbine blades permits the use of more intricate data transformations such as topological data analysis (TDA), which would otherwise be too computationally intensive for anomalies requiring detection within seconds. Additionally, this approach enables a more refined detection algorithm, crucial for identifying cases in which the ice distribution is symmetric across the wind turbine rotor, which does not produce imbalance loads in the structure and therefore has a subtler effect.