Blender has an Ivy Generator addon that lets you add foliage to any object.

Blender has a bunch of built-in addons, like a sapling and an ivy generator, that can be pretty useful. Pixxo 3D Juandre (Jay) Labuschagne walks through how to quickly turn on and use IvyGen to add Ivy to any surface or group of objects.

Going Further With Folliage in Blender

Previously, Daniele De Luca looked at how to build trees in Blender using the Sapling Tree Generator Addon, specifically how to style the leaves of the tree to look more customized. Curving and Styling Leaves With the Blender Sapling Addon.

Michel Anders was creating his Tree Addon for Blender. He uses the space colonization algorithm described and developed by Adam Runions. The space colonization algorithm can have tree model parameters corresponding visually to relevant tree characteristics identified in landscaping, offering convenient tree shape and structure control. Essentially the tree will grow in the space provided for it, much like it would in real life. Here is the article:  Addon for Blender Creates Trees Suited for Architectural Renders Based On The Space Colonization Algorithm.

Not really tree-based, but still within the same vein, we have Tamir Lousky, who once shared an Addon for Blender that will allow you to animate the growth of Ivy or any branching object. Check out Ivy Growth Animator for Blender Creates a Growing Effect in Blender Easily.