Why does walking soak my upper clothes?

Four months ago I started walking every day and have built up some stamina. I hadn't been able to exercise for years but I find my heart and lungs are rarely stressed, although if I begin to feel so I breathe from abdomen and fully exhale air.. When I return home my arms and upper body clothing is soaking wet. Warm or cold weather the same. Trousers are ok. I'm 59 yrs old. What's happening?