Observations and climate models have consistently shown a stronger surface warming in the Arctic than the global mean, a.k.a. Arctic amplification (AA), which has a strong asymmetry between the cold season and warm season. Previous studies suggested that key contributors to AA are the positive surface-albedo feedback and lapse-rate feedback. However, the lapse-rate feedback itself depends on temperature profiles and sea-ice loss. Whether sea-ice loss or lapse-rate feedback dominates the Arctic amplification remains an open question. Analysis of datasets based upon observations reveals a 1.11 K per decade surface warming trend in the Arctic (70-90°N) during 1979-2020 cold season (October-February) that is five times higher than the corresponding global mean. Based on surface energy budget analysis, we show that the largest contribution (~82%) to this cold season warming trend is attributed to changes in clear-sky downward longwave radiation. In contrast to that in Arctic summer and over tropics, lower-tropospheric inversions associated with the temperature and moisture profiles play a unique role in explaining changes to the downward longwave radiation. Our results suggest that Arctic lower-tropospheric stability should be considered in conjunction with sea-ice decline during the preceding warm season to explain Arctic amplification.