Emulsion hydrogels are promising materials for encapsulating and stabilizing high amounts of hydrophobic essential oils in hydrophilic matrices. In this work, clove oil-loaded hydrogels (CS/OP-C) are synthesized by combining covalent and physical cross-linking approaches. First, clove oil (CO) was emulsified and stabilized in a chitosan (CS) solution, which was further hardened by Schiff base covalent cross-linking with oxidized pullulan (OP). Second, the hydrogels were subjected to freeze–thaw cycles and, as a result, the clove oil was stabilized in physically cross-linked polymeric walls. Moreover, due to cryogelation, the obtained hydrogels exhibited sponge-like porous interconnected morphology (160–250 µm). By varying the clove oil content in the starting emulsion and the degree of cross-linking, the hydrogels displayed a high water retention capacity (swelling ratios between 1300 and 2000%), excellent elastic properties with fast shape recovery (20 s) after 70% compression, and controlled in vitro clove oil release in simulated skin conditions for 360 h. Furthermore, the prepared clove oil-loaded hydrogels had a strong scavenging activity of 83% and antibacterial and antifungal properties, showing a bacteriostatic effect after 48 and 72 h against S. aureus and E. coli. Our results recommend the new clove oil-embedded emulsion hydrogels as promising future materials for application as wound dressings.