Working outdoors for long periods of time with power tools that can create a large amount of noise which over time could damage your ears and possibly though unlikely cause deafness in later life. This can be prevented by wearing earmuffs. There is some danger with earmuffs however as you may not be able to hear people around you or most things happening around you which could have dire consequences while working with power tools so you need to put the extra effort in to be aware of your surroundings.
When working with chainsaws or especially axes there is a danger of splintering which most of the time would not be to dangerous could get into your eyes. This could potentially cause quite a lot of damage so its always a good idea to have goggles on in forestry.
Unless your hands are extremely callused when using a chainsaw or an axe you could get a lot of blisters on your hands and the easiest way to avoid this kind of injury is to wear safety gloves. This means you'll be able to work longer in a day than without them.