I am sending a pdf file with listed comments by line. Overall, you can consider most of them as suggestions and minor changes. As I used the climwin package and mixed models too, I can say that the methods and results are solid. The introduction is brief but clear, and the discussion is on the level with the results, avoiding too much guesswork given that the analyses are exploratory. However, maybe you underplayed a little bit the novelty of the study (specifically about the changing variables and time windows over time), which should deserve emphasis in the discussion/conclusion. Having said that, consider that I have a blindspot: I am biased to understand your methods easily, so please consider the potential criticism of other reviewers that are may not be familiarised with the climwin approach to make it as clear as possible for them.

ABSTRACT
States exactly what the ms presents. No suggestions.
INTRODUCTION
Generally, it is very clear, brief, and easy to read. The objectives and predictions are also very clear.
L28-30. It is not very clear what you mean.
L56. You use ‘ice-cover’ around 20 times in the ms to substitute ‘sea ice-cover’ (excluding the Supplement). Maybe it is worth using ‘sea ice-cover’ throughout (~80 additional characters) to avoid confusion to some readers.
METHODS
Some reviewers may find the Methods a bit too long but sliding window approaches really need a lot of detail and the authors provide everything necessary for its understanding in an organized way.
L110 Insert a hyphen between ‘ice’ and ‘cover’ for consistency
L124 Change ‘http’ to ‘https’
L126 You can and preferably omit the /index_e.html. Use this instead: https://climate.weather.gc.ca
L131 The page mentioned is redirecting to https://www.ncdc.noaa.gov/cdo-web/search. Is this correct?
L142 Maybe change the wording from ‘with a fixed effect predictor of age’ to ‘with age as a fixed effect predictor’ because ‘predictor of age’ may cause some confusion as something predicting age for readers not versed in these models.
RESULTS
Clear and organized. No suggestions.
DISCUSSION
Well detailed and encompasses many of the questions the reader may think. Conclusions sum up very well the message from the ms.
FIGURES and TABLES
Very nice and publishing-ready

SUPPLEMENTAL INFORMATION
I did not have the time to read in detail, but at first glance, it seems nice with a very welcome Table of Contents.