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High-throughput screening enabled by structure-property prediction models is a powerful approach for accelerating materials discovery. However, while machine learning of structure-property models have become widespread, its application to mixtures remains limited due to increased complexity and the scarcity of available data. Machine learning methods for high-throughput screening of eutectic mixtures have been proposed in recent years, but there remain challenges due to the lack of diverse, open-access datasets and the need for feature engineering based on chemical knowledge. To overcome these limitations, we propose a method using Siamese graph neural networks trained solely on structural information, without requiring any prior chemical descriptors, to predict eutectic melting temperatures. We demonstrate on a dataset of molten salt eutectics that this approach can reach similar performance to chemistry-based models that require significantly more prior knowledge. We show that lower-order mixtures may be used to augment data on higher-order mixtures. Interestingly, our model trained on inorganic molten salts seems to learn information about the ideal mixture model. We also evaluate the efficacy of using our inorganic molten salt model for transfer learning with a variety of organic eutectic mixtures.