Arctic atmospheric circulation and near-surface temperature are physically coupled, yet it remains unclear whether their spatial coherence changes in the same way across seasons. Using ERA5 reanalysis for 1940-2024, we directly compare winter (DJF) and summer (JJA) anomalies of 500 hPa geopotential height (Z500) and 2 m air temperature (T2M) over the Arctic. We combine threshold-independent correlation-decay analysis with fixed-density climate networks to quantify both the geographical extent of coherence and the spatial organization of the strongest relationships. The two fields exhibit opposite seasonal behavior. Z500 is more spatially coherent in winter, with its characteristic correlation length decreasing from approximately 1728 km in DJF to 1259 km in JJA. T2M shows the reverse pattern, with its correlation length increasing from approximately 1275 km in DJF to 1778 km in JJA. Climate-network analysis locates these changes geographically: winter Z500 connectivity is broadly distributed across the Arctic, whereas summer T2M connectivity strengthens and expands over the central Arctic Ocean. The seasonal transition, therefore, does not produce a uniform change in Arctic atmospheric organization. Instead, it is characterized by stronger basin-scale dynamical coherence in winter and enhanced near-surface thermodynamic coherence in summer. By comparing circulation and temperature within a common quantitative framework, this study demonstrates that physical coupling does not imply parallel seasonal organization and provides a baseline for assessing future changes in the spatial structure of Arctic atmospheric variability.