You have to consider several things before using shredded trees as ground fill in your arena:
1. Do you know the source of the tree/bark? If it (or any of it) originates from black walnut or other trees known to be toxic to horses, you definitely do not want to use it, or you will have more problems than you have solved.
2. What is the size of the shredded material? If "rough shred" material, sometimes referred to as hog fuel, is used in footing areas, it can end up freezing in an "up" position after a hard freeze and cause abscess, bruising, and lameness troubles.
3. Also, depending upon how the footing is processed or how deep it is, sometimes bark/mulch can get slippery if it gets too wet and/or frozen.
Aside from that, with any organic material, there will be decomposition, so its effectiveness of fill may be time dependent.
