Just about any manufacturer of horse fence will include a disclaimer that no fence is completely safe. Many horses will, and do find ways of proving that. Barbed wire, for the obvious reasons, regular 14, 16, and 18 gauge hot wire because they can kink and wrap around legs if a horse isn't trained to respect them. High tensile (12 gauge) is less likely to wrap around legs but if it is not hot a horse can still squeeze right through. Wood can splinter and like mentioned before can encourage chewing and possibly cribbing (which is a bad habit, different than chewing). I have seen the vinyl coated high tensile make a mess out of a horse too because it caused MAJOR rug-type burns on horses who freaked, tried to jump it and ended up on both sides of it.
I personally feel hot high tensile is the best but I don't even have it yet for mine, they make do with hot wire that is 14 gauge. I think that training a horse to respect fences is the best thing you can do to prevent injuries. If they respect fences they simply avoid testing it and finding ways to hurt themselves. That is easily said, not so easily done. You will be able to help your horse be safe by making sure that the consequences of touching the fence are enough to discourage it from further investigation. I have three horses, one is so afraid of electric fence that getting him through a gate is difficult on a halter and lead rope. Another is always waiting for a weak spot and will go through a hot fence if it isn't REALLY hot and yet the third we have yet to see. I just got her and all I know now is that SO FAR she has stayed in. I will, over the next summer, start replacing our ageing wire with electrified high tensile, it is almost impossible to kink and springs back if a horse should try and bolt through it (we have moose and deer make a mess out of our fence each winter). I am experienced with the different kinds of vinyl coated 'horse safe' fence from the boarding stable I managed. We had a mixture of products and the wide (looks like boards) vinyl seems like a good option but you still need some hot wire to discourage lean-through grazing, the stuff on the farm was also approaching 15 years old by the time I came on and it had a tendency to splinter into sharp pieces (I hope that is not the case with the product anymore now that there are better UV inhibitors out there). You will find that any product designed to be electrified is dangerous if it is not hot. That includes wire, poly twine, horse braid rope, and electric tape. We still have to make a choice and doing the best for your horses personality will do you the most good.
Do the best you can and give your horse the most space and food as necessary to keep them happy where they are. I would personally avoid, at all costs, barbed wire and any kind of field fence (mesh) with holes big enough to catch a horses foot. On a final note, any fence that lets a horse get out (even if they don't get hurt from it) is NOT horse safe and you don't want your best friend running up and down the road to get hit by a car.
Thank god you are asking questions, you are on the right track and very concisentous! (can't even spell it close enough for spell check)