A convenient method for the preparation of polybasic ternary hybrid cryogels consisting of Halloysite nanotubes (HNTs) and tertiary amine functional groups by freezing-induced gelation is proposed. Ternary hybrid gels were produced via one-shot radical terpolymerization of 2-hydroxyethyl methacrylate (HEMA), 2-acrylamido-2-methyl-1-propane sulfonic acid (AMPS), and DEAEMA in the presence of HNTs. The equilibrium swelling in various swelling media and the mechanical properties of the produced ternary hybrid gels were analyzed to investigate their network structure and determine their final performance. The swelling ratio of HNT-free gels was significantly higher than the ternary hybrid gels composed of high amount of HNTs. The addition of HNTs to terpolymer network did not suppress pH- and temperature-sensitive behavior. While DEAEMA groups were effective for pH-sensitive swelling, it was determined that both HEMA and DEAEMA groups were effective in temperature-sensitive swelling. Ternary hybrid gels simultaneously demonstrated both negative and positive temperature-responsive swelling behavior. The swelling ratio changed considerably according to swelling temperature. Both DEAEMA and HEMA monomers in terpolymer structure were dominant in temperature-sensitive swelling. Mechanical tests in compression of both as-prepared and swollen-state demonstrated that strength and modulus of hybrid cryogels significantly increased with addition of HNTs without significant loss of mechanical strength. Ultimately, the results of the current system can benefit characterization with analysis tools for the application of innovative materials.