The growth of the Internet of Things (IoT) networks brings with it a number of issues when it comes to safeguarding sensitive data in the context of Artificial Intelligence (AI) based data processing. This paper presents a homomorphic encryption based AI system that can be used to provide privacy-preserving IoT analytics in an integrated sensing, edge computing and cloud intelligence architecture. The framework proposed is based on Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) models, which are also equipped with encrypted inference mechanisms, allowing for the secure analytical performance of operations without revealing the plaintext sensor information. Ciphertext packing, adaptive precision reduction, model pruning, encrypted batch inference and parallel processing are discussed as approaches to address computational optimization. The reported comparative evaluation shows that the proposed encrypted AI framework has an accuracy of 96.2%, precision of 95.4%, recall of 94.7%, and F1 score of 95.0% while conventional AI processing has an accuracy of 97.6%, precision of 96.8%, recall of 96.1%, and F1 score of 96.4%. Compared to the reported data privacy level, the improvement is from 72.5% to 99.1% (a gain of 26.6 percentage points) with only 1.4 percentage point drop in the classification accuracy. These results show that the reported privacy measure and the predictive performance have a good trade-off. The framework could serve as a basis for privacy-preserving intelligent analytics in applications such as healthcare, smart cities and industrial IoT.