## 5 Limitations and Further Research  
Limitations of the present study include the small group size mentioned earlier. The obtained results should, therefore, be treated with caution (as a pilot study). During the study preparation and result analysis, efforts were made to reduce the risk of type I errors (showing significant differences that do not actually exist). However, it is likely that not all the changes that occur during winter swimming have been captured (type II error). According to G*Power software analyses (ver 3.1.9.7), obtaining high-power parametric test resultsfor repeated measurements (effect size: \(f=0.25\); \(\alpha=0.05\); power (\(1-\beta\)) = 0.80; number of groups: 2; number of measurements: 2) would require a sample size of 98 individuals, which is very difficult to achieve in the case of winter swimmers.  
Winter swimmers are a group that is not easily accessible: there is only one club for winter swimmers in the city where the study was conducted. Virtually all winter swimmers meeting the eligibility criteria were included in the presented study. Given the difficulties in recruiting winter swimmers for scientific research, if it is not possible to involve a larger group in further studies, the number of measurements should be increased. This should allow to reduce the minimum sample size while maintaining high test power [42].  
The fact that women were not investigated is another limitation of the presented study.  
Not implementing the second measurement in the control group (monitoring of emotional states) can be considered a further limitation. The research team was not able to investigate this owing to human resource constraints: it was impossible to carry out two measurements at two different locations at the same time. In further studies, two options can be suggested: (1) to examine mood states in the control group at the same time as among the winter swimmers; (2) to invite the control group individuals to a swimming pool with warm (air-temperature) water, adjust the swimming time, etc., to winter swimmers, and take measurements after the participants leave the water.  
In future studies, it would be advisable to test the long-term effect of winter swimming, e.g., over an entire season. The research presented here mainly focused on short-term results arising from a single cold-water immersion. Although differences between winter swimmers and the control group were examined, this was only a cross-sectional evaluation, which did not allow us to identify a cause-effect relationship.  
Conceptualization, A.T., K.W. and J.B.; Methodology, A.T.; Validation, A.T.; Formal analysis, K.W.; Investigation, A.T.; Resources, A.T.; Data curation, A.T.; Writing--original draft, A.T. and K.W.; Writing--review and editing, A.T. and K.W.; Supervision, J.B.; Project administration, A.T.; Funding acquisition, A.T. All authors contributed equally to this manuscript and share first authorship. All authors have read and agreed to the published version of the manuscript.  
The project was funded within the statutory research project No. 50/PB/RID/2023, and this publication was financed within the program of the Minister of Science under the name 'Regional Excellence Initiative' in the years 2024-2027, project number RID/SP/0027/2024/01, in the amount of PLN 4,053,904.00.  
This study was approved by the Bioethical Committee of the Regional Medical Chamber in Krakow (226/KBL/OIL/2023, 8 July 2023).  
Informed Consent Statement: Informed consent was obtained from all subjects involved in this study.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors would like to thank the winter swimmers from the Krakow Society of Winter Swimmers 'Kaloryfer'.  
The authors declare no competing interests.