I am not on HT, but after a lousy winter of colds and coughs, my GP found my testosterone was very, very low. After a fight with endocrinology (and with the backing of my urologist), I was put on testosterone therapy....BUT.....now it is possible it is messing up my haemoglobin levels so I may have to come off it again. Back to lousy winters.
I did look for the evidence connecting testosterone with PCa and it did seem to be tenuous, even suggesting the original connection was from a sample size of one person back in the 1940s.