I agree that ANY wood in contact with the ground should be protected. However, I would protect the entire structure, not just the parts in the ground. By treating the entire structure with some sort of preservative, you will avoid any moisture wicking down through the wood from the top, when it rains for instance. My theory is that by prtecting the bottom only you are creating a sort of bathtub for water to sit in.
One of the better woods for outdoor use is mahogany. There are several grades. Some inexpensive, while some are very expensive. But look at it this way. If you purchase a piece of IPE' for example, a very hard and durable form of mahogany, the amount of 3/4" square boards you can cut it into to build a trestle will make up for the cost of the material.
I have been using a mixture of boiled linseed oil and turpentine to treat my outdoor wood. Whether it's something in my garden railway or wheelbarrow handles. I even use it on the unpainted metal parts of outdoor tools, as it is a good rust preventative. And bets of all, it's a natural product, not a chemical. Use about 2/3 linseed oil and 1/3 turpentine. This way you can brush it on easily. The turpentine thins the oil and allows it to penetrate better.