The problem is the concept of ‘depressing/weakening/reducing the immune system’.
It rolls off the tongue so easily and seems to have become part of the language, but no-one actually knows what it means.
The ‘immune system’ is a complex physical and chemical and biological entity that is relatively poorly understood even by the clever folk, and to suggest that going out on a bike and getting cold feet is going to cause it problems is a bit daft.
I deal with people who have actual, real, provable problems with their ‘immune systems’, and also deal with people who get their core temperatures manipulated one way or another, and my experience is not the same as a few bikers who get a bit chilly…