How can I prevent animals from eating my wooden swingset?
Something about the wood is attracting the animals, you are going to have to find a way to make it less appealing either by taste or smell, the only other way to deal with it is to protect the wood with some sort of armor. By far the most cost-effective and quickest way to do this is to sprat the wood with something like ROPEL, rub the wood down with a bar of hand soap, or coat it with chili spray.

If you're worried about the sprays harming the wood then you'll need to seal the wood with an outdoor varnish. Really you should do this anyway as without it the wood will weather and rot much more quickly. It's possible that varnishing it will make it less attractive to the animals in the first place as it will certainly not taste good. 

You're going to have to accept that you need to do something to the wood that might change the character of it to keep it from getting nibbled to bits. The sooner you do it the more of it will be left.