Hmm - difficult to know what to do when a tree is covered in ivy like that.
If its growing in a forest completely covered by ivy, and the ivy is spreading quite rapidly, then it is probably a good idea to remove it. The best way to do this is just to sever the stems at ground level, and then leave the ivy to rot and fall away (pulling it off can damage the tree's bark, but dead ivy up the stem will do no harm.
However, in many cases, ivy is opportunistic, and will tend to only get a good hold on trees that are already dying, since normally their own size and leaf cover makes it difficult for ivy to get established.
The best thing to check is whether the tree (and inparticular) the crown is healthy. If it looks in good condition, then cutting away the ivy is fine (if you don't want to completely kill the ivy, then cutting it back at least to the base of the crown is all that is needed to allow the tree enough space to continue putting out new shoots and tender branches). If it isn't looking in good condition, then it might be better to just let nature take its course. At the end of the day, ivy is just as useful to the ecology of a forest as a fruit tree, even if it is less useful to us!