The Stats Zone did a detailed statistical analysis of the effect of a summer football season versus a winter one, here:
https://www.thestatszone.com/archive...s-europe-13762
In reading it, I would urge the following cautions:
1. It's five years old;
2. It reallly only covers three countries - Den (Winter) and Nor & Swe (Summer);
3. It only covers a relatively small number of clubs over a comparatively short period, meaning that one or two particularly well-run clubs could skew the results - see eg FC Mitjelland.
Therefore it may suffer from having too small a sample size as to be reliable.
All that said, here is a summarised version of their conclusion:
"To conclude, we have looked at Scandinavian teams’ performance in the European cup competitions and split it by summer and winter leagues. From our data we cannot say that there seems to be an advantage to playing in a summer league when it comes to European qualifiers. In fact, Danish sides figure more frequently in the tournaments and on average perform better when they do... ... So in terms of raising the European Cup performance, could it potentially be a wise move for Norwegian and Swedish teams to consider playing similar format to the winter leagues?"
P.S. I'm pretty sure Denmark used to operate a summer season, then switched to a winter season a few years back, though I can't find out exactly when.
EDIT: The Danish League was a summer one from 1958, switching to a winter league for 1991/92.
[Also, Danish professionals playing outside the country were prevented from playing for the (amateur) National Team until 1971, with the domestic league only permitting professionalism from 1979.]