If you are riding at that temp then money shouldn't be an issue, if it is then stop riding when it is so cold. If you let you feet go numb you are going to get sick.
Can you share some peer-reviewed research on this statement? It might be how you feel after getting cold enough to lose feeling in your feet, but I don't know of any research that shows a
causal relation. We get sick from interactions with sick people, not from being cold.
FWIW I avoid numb feet cause it's painful and can cause tissue damage, and that's reason enough ... that said, I usually get home from a ride a couple times a year with some loss of feeling in my feet, but can't think of one time I got sick.