Apple pomace, a by-product of juice production, is a rich source of dietary fiber and bioactive compounds, making it a promising functional ingredient for bakery applications. This study evaluated the physicochemical and sensory properties of shortbread cookies enriched with apple pomace dried under different conditions, while also analyzing the drying process, focusing on drying kinetics and powder characteristics. Pomace dried by either contact drying or freeze-drying was ground and used to replace 20% of wheat flour in the cookie formulation. Drying kinetics were best described by the modified Page model, and freeze-dried pomace showed higher grindability than contact-dried samples. Cookies enriched with pomace exhibited similar overall composition, with differences mainly observed in fiber content (9.82–11.75%). Those containing freeze-dried pomace were lighter, with reduced red and increased yellow tones, and were firmer, requiring approximately 30% higher cutting force. Despite differences in physical properties, enriched cookies were consistently rated higher in overall acceptability than the controls. The results indicate that the drying method and temperature influence the physicochemical properties of apple by-product and the resulting cookies, while having mainly minor effects on sensory acceptance, confirming the potential of apple pomace as a functional ingredient in bakery products.