This study aimed to evaluate the effect of two-year storage of varietal honeys (buckwheat, linden, rapeseed, honeydew, and multifloral) at various temperatures (4 °C, −18 °C, −40 °C, and −80 °C) on the content of 5-hydroxymethylfurfural (5-HMF), diastase number (DN), and color assessed in the CIE L*a*b* system. The control samples were stored at room temperature (RT, ca. 20 °C). The results indicate that storing honey at low temperatures effectively mitigates undesirable quality changes, particularly enzymatic degradation and color alterations, while preventing excessive 5-HMF accumulation. After storage, a significant (p ˂ 0.01) decrease was noted in the diastase number (DN) of the honeys, regardless of the temperature (by ca. 66.7% at RT and by 53.1% to 58.3% at low temperatures, p > 0.05). Low storage temperatures led to higher enzymatic activity in buckwheat, linden, and honeydew honeys compared to rapeseed honeys. RT significantly (p ˂ 0.01) increased 5-HMF concentration by 79.3%, whereas the cold and frozen storage conditions increased 5-HMF concentration only by 25.1% at −18 °C and 33.2% at 4 °C. The greatest color changes manifested by significant (p ˂ 0.01) darkening, with a decrease in the h° value (p ˂ 0.01), and a lower contribution of the yellow color and a greater contribution of red color (p > 0.05) in the color profile were noted in the honeys stored at RT. Storage at this temperature resulted in a significantly (p ˂ 0.01) higher total color difference of the honeys (ΔE = 9.53) compared to the other temperatures tested (3.71 < ΔE < 5.58). The low storage temperatures may elicit a positive and comparable effect on preserving the satisfactory quality of the analyzed varietal honeys. It is noteworthy that this positive effect could already be achieved at a storage temperature of +4 °C without the need to apply frozen storage temperatures, which is essential given the economic and environmental concerns.