Statistically, long hot summers have been followed as often by mild winters as by cold ones. There is little correlation between the amount of precipitation or temperature in the winter and summer temperatures.
If the hot summer comes from a persistent high pressure system, the subsequent winter is likely to be cooler, since high pressure systems prevent cloud cover. If the high pressure system persists through the fall and winter, there will be insufficient cloud cover to prevent ground heat from escaping. This causes a colder winter. However, the high pressure system is as likely to disperse as it is to linger, which means that its presence during the summer months does not guarantee a subsequent cold winter.