Among recent trends in the coffee market, cold brew beverages stand out, prepared using various techniques where the coffee-to-water ratio, temperature, and extraction time significantly influence their bioactive and sensory properties. The aim of this study was to prepare functional cold brew beverages from Arabica and Robusta coffee, enriched with the addition of green coffee, ground ivy (Glechoma hederacea L.), and mountain germander (Teucrium montanum L.). The beverages were prepared at 15 °C and 25 °C. The bioactive characterization of the coffees and beverages was determined using spectrophotometric methods and high-performance liquid chromatography with photodiode array detection (HPLC-PDA). Robusta coffee had a higher content of melanoidins, total polyphenols, caffeine, and chlorogenic acids, as well as a more pronounced antioxidant capacity compared to Arabica coffee. Cold brew beverages prepared at the higher temperature (25 °C) were characterized by a higher content of melanoidins, polyphenols, and caffeine, along with a higher antioxidant capacity compared to beverages prepared at the lower temperature (15 °C), which also received lower sensory evaluations. The functional cold brew coffee beverage with the addition of mountain germander was the least well-received by the sensory panel.