I'll start with a map showing the frequency of warm and cold extremes during El Niño winters, regardless of the PDO phase - see the first image below. I've defined the extreme thresholds as the 2nd and 98th percentiles of the daily historical distribution of daily mean temperature, so the thresholds are different for every day and are equally likely to be exceeded at any time of year. The columns on the map show the frequency of exceedance for 22 winters with the highest November-March mean Oceanic Niño Index, i.e. the warmest one-third of winters since 1950 in the Niño3.4 region of the equatorial Pacific Ocean. The heights of the columns show the exceedance frequency, with the horizontal dotted line indicating the long-term normal frequency of 2% (i.e. 3 days per winter).
As expected, warm extremes are more common than normal, and more common than cold extremes, during El Niño winters in south-central and southeastern Alaska. This matches the sign of the seasonal mean temperature signal. However, in western Alaska - and in Fairbanks - cold extremes are nearly as common as warm extremes, and neither is more common than normal, despite the fact that El Niño winters are more often warmer than normal overall.
If we look only at El Niño winters when the PDO is also in the top one-third of the historical range, the warm signal is much more widespread and is overwhelming in the south-central and southeast; cold extremes are almost unheard of when the oceanic temperature patterns show these anomalies.
Looking at the same analysis for La Niña winters, the results show that cold extremes are more common than normal and more common than warm extremes at every location; the cold signal includes western Alaska, unlike El Niño's warm signal. However, it's interesting to note that the frequency of warm extremes is not reduced compared to normal from Anchorage to Barrow and throughout the interior; this is a result of increased variance during La Niña winters.
A negative PDO phase boosts the chances of very unusual cold conditions during La Niña, but the frequency of warm extremes still remains near-normal in the central part of the state; this is quite surprising, as I would expect these winters to be overwhelmingly cold. It seems that, at least for the interior, a negative PDO is nowhere near as effective in amplifying La Niña cold as a positive PDO is in boosting El Niño warmth.
When La Niña is not accompanied by a negative PDO phase, the cold signal goes away and most locations see slightly higher chances of warm extremes than cold extremes. Again it's notable that the PDO signal does not overwhelm the La Niña signal as it does for El Niño. We might conclude that the PDO phase is less significant for Alaska's winter temperatures when La Niña is in play, and more significant during El Niño conditions; or alternatively we could say that La Niña is more reliably connected to unusual temperatures than El Niño.
Here is a corresponding set of maps conditioned on a positive or negative PDO phase, with or without El Niño and La Niña. A noteworthy point here is that, during positive PDO winters, warm extremes are more common in the southwest (Bethel, St Paul, Cold Bay) when El Niño is not observed. Similarly, during negative PDO winters, warm extremes are actually more common from Anchorage to Kotzebue and in the central interior during La Niña than during non-La Niña winters.
And finally, two maps showing the frequency of extremes for neutral PDO winters and neutral ENSO winters. Notice that cold extremes are less common than warm extremes in many locations when the ENSO phase is near neutral.