MIKE MOSS SAYS:    Brenda,    There isn't a real clear relationship that consistently links temperature anomalies for a given winter to the departures from normal experienced the previous summer. There may be some situations in which a persistent large scale forcing system like El Nino or La Nina lasts throughout multiple seasons and exerts an influence such that the two would be related more firmly. However, in many cases the intensity and sign of those large scale patterns can change between one season and another.

This doesn't represent a rigorous investigation by any means, but just to get an example from relatively recent history I went back and looked for summers with temperatures that were at least 1.5 degrees above or below normal for our region during the period 1975 - 2006. There were 9 such summers during that span. In three cases, the winter temperature departure from normal was the same sign as the summer departure (i.e. cold summer followed by cold winter or vice versa), in five cases the winter departure was the opposite sign  (warm summer followed by cold winter or vice versa), and in one case the winter departure was very nearly zero. I did note that of the five summers in the sample that were well above normal, four were followed by cooler than normal winters. So while there's a lot of variety in the responses, you could at least say that within that span of years, an unusually warm summer was often followed by a cooler than normal winter.