As of early October, the 2017 Atlantic hurricane season has produced 14 named storms, 8 of which have reached hurricane strength, and 5 of those major hurricane status (Category 3 or higher). Regarding storm numbers, this year is still below the average (since 1995) of 16 named storms for both neutral ENSO years and La Niña years (a La Niña is developing this year), but already at the average for hurricanes and one storm ahead of the average for major hurricanes.
Since there are still a few more weeks to go before the season quiets down for the year, we will likely end up near the average regarding storm numbers this year, and likely above the average for hurricanes. More notable is that we have seen some long-lived major hurricanes this year, which has pushed the seasonal ACE index to well above normal levels. The ACE, or Accumulated Cyclone Energy index, essentially combines the number, duration, and intensity of storms into a single index. As of early October, the ACE index for the Atlantic basin in 2017 was 202, good for 6th place all-time. Of the 202 ACE units, 153 of them were the result of just three storms: Irma, Maria, and Jose. If you take out those three storms, the ACE for this year would be running 2nd lowest on record. However, it is not unusual for the ACE index to be dominated each year by a couple of major storms. Note that the highest ever ACE index for a year was 250 in 2005, though it took 28 storms to reach that total in 2005.
So, does the active hurricane season this year, regarding ACE index, mean anything for the upcoming winter season? Well, not really. The following plot shows US population weighted winter temperatures versus ACE index for the last 30 years or so. The data is scattered quite evenly, with only a very slight positive trend to the data. There does seem to be a tendency for moderately less active hurricane seasons to be followed by colder winters (cold winters seem to dominate when the ACE is between 50-100), but warm winters are only slightly more frequent when the ACE is over 100. So, there may be a slight tendency for warmer winters following a more active hurricane season. However, since active hurricane seasons tend to occur in years when the Atlantic basin is warmer than normal, the warm water temperatures may contribute more to any warming influence than the hurricane activity itself.
So, in summary, Atlantic hurricane activity seems to have limited impact on winter temperature trends, though cold winters seem to be more frequent when tropical activity is a little below normal. Western Pacific tropical activity appears to have a more significant influence on winter temperature patterns and colder than normal US winters seem to occur more frequently when tropical activity is below normal in that region. However, since the location and intensity of tropical convection in the Pacific (regarding both typhoons and regular thunderstorms) are influenced by ocean temperature patterns and ENSO phase, how much of the influence is directly the result of tropical activity versus the underlying ocean temperature patterns is not certain. But if there is some modulating influence from western Pacific tropical activity, then the below normal activity in that region thus far this year may help to increase the odds for colder weather this winter across the US, at least slightly.