Feedback between the North Atlantic Oscillation (NAO) and winter sea ice variability is detected and quantified using approximately thirty 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 sector (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 northeast of Greenland. In weekly data for December through April, the VAR indicates that NAO index (N) anomalies cause like-signed anomalies of the 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 time scale of G. The presence of feedback in the system following realistic local maxima of N and G can shift the expected value of the evolving N and G by up to 0.32 and 0.49 standard deviations, respectively. If G is maintained at a constant large value, N asymptotically approaches -0.14 times that value -- a result we show analytically using the relations in the VAR. The relevance of these results to intraseasonal and interannual NAO and sea ice variability is discussed.