For a better LOESS fit (i.e., to eliminate the end effects), I would do as you have done, plotting data from January to December, using a smoothing value of 61 days (or maybe 31, if the winter and summer extremes were flattened too much). Then I would rearrange the data so it goes from July to June and repeat the LOESS. Smoothing values for the spring and summer should be the same, so I would combine April to September of the January-December smoothing with October to March of the July-June smoothing.

Then, since I'm interested in winter temperatures, I'd do my main chart from July to June.