I fell timber professionally for 13 years and myself and the rest of the guys carried their chainsaws on their shoulders. Most of us wore leather pads. Since most of my career was spent working on the rugged West Coast for a helicopter we had to cover long distances on nasty ground mostly using 660, 395 size chainsaws with 32-36" bars, with stints every now and then running 088, 3120 size saws with 36"-84" bars. The safety guys used to come around and tell us to roll the chain off and wrap it around the handlebar before we carried it on our shoulder but that can be a hassle every time you need to cover some ground, so I would not do it all the time. I admit I got a few wounds from carrying my saw on my shoulder with the chain on, but the alternative sucks! After taking a few spills with my saw on my shoulder(mostly in the beginning of my career) I started reading the ground a lot better, and when the ground got rough, or brushy, I would carry the saw at my side by the handlebar, and sometimes if the ground was consistently rugged and I had a long hike in with my saw I would roll the chain off, and wrap it around the handle. I Fell timber on some gnarly helicopter ground, so I really had to learn my footing. Also I have my own custom shoulder pad that works great for not only protecting your shoulder, but your neck too. It is just the top cut off of an old pair of cork boots(right at the ankle so you already have a natural bend where shoulder meets neck) This is not the best picture of it, but it is the best that I currently have.
Shoulder pad