I think we can quite confidently say that this cherry tree in the woods has not been cleared of ivy for a while. It is now unclear whether it is an ivy tree with associated cherry or a cherry tree with associated ivy. Common Ivy or Hedera helix is unusual in that it is a plant with two distinct stages of growth. Its first or juvenile stage is when it climbs, its leaves are 3 to 5 lobed and self clinging stems wind their way up the tree sometimes to 3om. When they reach the light the adult or arboreal stage begins and the leaves become complete, that is unlobbed, and the habit changes to a more bushy one. This is when the umbels of greenish yellow flowers are produced. These flowers are very popular with insects but apparently honey produced from these flowers tastes like disinfectant, I have it on very good authority, mind you if that is your thing you may enjoy it. The resultant shiny black fruit are a valuable food source for birds, but beware they are poisonous to humans so it is just as well the temptation is usually high up away from snacking gardeners. Outside the potting shed the wood pigeons, who remind me of pantomime dames, crash land onto a nearby ivy covered fence and pluck them off before tumbling away. The thick vegetation also provides a secure habitat for many insects, small mammals and birds.
Of course it will also travel across open ground and sprawl over banks in its search for a suitable climbing frame, forming a dense ground cover. It is generally considered unlikely that ivy will damage a healthy tree, it is probable that a tree that becomes overwhelmed, such as the above cherry, is already in decline, the loss of canopy allowing more light in and the ivy to thrive. On a negative point, it can cause problems in severe weather conditions by increasing the sail effect, especially in deciduous trees during winter, making them more vulnerable to falling in high winds. Also aesthetically, in the formal garden, a clean bole is often thought more attractive, but this is a question of taste. If things do get out of hand on a prized specimen it is easy enough to cut or saw through the main stems and there are hours of pleasure to be had peeling off the tiny adventitious roots from the trunk.