Progressive climate change may have unpredictable consequences for the Arctic environment. Permafrost catchments off the west coast of Svalbard, described as “thin” and “warm,” are particularly sensitive to climate change. The interdisciplinary research on the hydrochemical response of surface and underground water functioning within a small permafrost catchment area focused on the determination of the impact of meteorological conditions (temperature (T), precipitation (P)) on the mean daily discharge (Q), and the lowering of the groundwater table (H). We determined physical and chemical properties (pH and SEC) and concentrations of major elements (Ca, Mg, Na, K) and 23 trace elements (i.a. Cd, Cu, Hg, Pb, Zn) in 280 water samples. The results of the correlation matrix showed that an increase in the average air temperature in the summer of 2021 had a significant impact on the hydrochemistry of both types of waters operating in the catchment. In response to increase in T, the lowering of the H (0.52 < r < 0.66) and a decrease in Q (−0.66 < r < −0.68) were observed what in consequence also leads to changes in water chemistry. The principal component analysis (CA) indicates that chemical weathering and binding of elements to DOC are processes influencing water chemistry. Results of statistical analysis showed that the resultant of the hydrometeorological conditions that prevailed in that season and the type of geological formations on which they were located had a significant impact on the water chemistry at individual measurement points. Significant differences in the concentrations of elements between points on the same geological formations were also found.