Yes, adult geese will damage young fruit trees in the autumn and winter months by pulling off the bark. Goslings won’t usually bother with trees.
It is a good idea to put a little chicken wire or plastic spirals designed to protect bark from animals such as rabbits around each tree trunk until the trees have grown large enough and the bark is tough enough. Even adult trees can get nibbled by geese (they love pulling at anything they can get their beaks around) so you may be better off keeping chicken wire around the trunk for life. This will also give added protection from rabbits and other animals that might chew the bark as well as geese.
Geese are inquisitive and will nibble almost anything so ensure that whatever you use cannot break into pieces and there are no pieces of string, wire or netting staples that can be pulled out and swallowed.
When fruit trees are planted, if chickens are also in the same area, they will scratch up the soil around the roots of the tree looking for food so chicken wire can double up as protection against this as well as protection from geese. This is why the chicken wire in the photo is covering such a wide area.