Numerous studies have revealed evidence that winter climate in the Northern Hemisphere is related to the solar cycle and space weather. Most of the studies investigating the impact of space weather on the North Atlantic Oscillation and Artic Oscillation indices (NAOIs and AOIs) analyzed monthly or seasonal data. In this work, we evaluated the responses of winter NAOI/AOI to space weather changes on the day‐to‐day timescale during 1950–2020 by using an autoregressive (AR) model with additional predictors, such as month, linear trend, trends of solar irradiance and Kp indices, the Quasi‐Biennial Oscillation (QBO) and El Niño–Southern Oscillation, the presence of sudden stratospheric warming (SSW) and high stratospheric aerosol loading (HSAL), and space weather variables, reflecting the day‐to‐day effect. Winter daily NAOI (AOI) follows the AR model of the 4th (5th) order. We found a positive day‐to‐day effect of Kp, solar wind speed (SWS) > 300 km/s, By ≤ 3.15 nT, and solar wind dynamic pressure (P) with a lag of 2 days on the NAOI and the AOI. For the AOI, additionally, the period of 1 day before–2 days after the solar proton event onset had a negative effect, and the signal of Kp and SWS was observed only for the east QBO phase. For the NAOI, a stronger effect of P was found on the presence of a strongly positive QBO phase. A stronger signal of Kp and SWS was found during HSAL. The signal of SWS > 300 km/s on the NAOI/AOI was different in sign during the periods with and without SSW.