I agree that this sounds like obsessional behaviour and the first thing to do is stop it happening. The more dogs practise a behaviour, the stronger it becomes.

Your friend needs to seek the help of a behaviourist but in the meantime I'd avoid trigger situations/objects by keeping him onlead and/or distracting with toys. Maybe go somewhere new and see if it's trees per sé or simply the particular trees he's got used to savaging?