Feedback between the North Atlantic Oscillation (NAO) and winter sea ice variability is detected and quantified using approximately 30 years of observations, a vector autoregressive model (VAR), and testable definitions of Granger causality and feedback. Sea ice variability is quantified based on the leading empirical orthogonal function of sea ice concentration over the North Atlantic [the Greenland Sea ice dipole (GSD)], which, in its positive polarity, has anomalously high sea ice concentrations in the Labrador Sea region to the southwest of Greenland and low sea ice concentrations in the Barents Sea region to the northeast of Greenland. In weekly data for December through April, the VAR indicates that NAO index (N) anomalies cause like-signed anomalies of the standardized GSD index (G), and that G anomalies in turn cause oppositely signed anomalies of N. This negative feedback process operates explicitly on lags of up to four weeks in the VAR but can generate more persistent effects because of the autocorrelation of G. Synthetic data are generated with the VAR to quantify the effects of feedback following realistic local maxima of N and G, and also for sustained high values of G. Feedback can change the expected value of evolving system variables by as much as a half a standard deviation, and the relevance of these results to intraseasonal and interannual NAO and sea ice variability is discussed.