Yep, as a general rule, the bigger issue is generally whether or not the tree is big enough to actually cover your body. That changes some with larger calibers though. Years ago, I played with some old 30-06 ball ammo. It went right through pecan trees over a foot in diameter and pecan is a lot harder than pine. Aside from being a larger projectile, those bullets had thicker jackets than 5.56 ammo designed to fragment. I have also used a 45-70 loaded with 405 grain softnose to "chop down" a couple of smaller oaks that were maybe 10" or so in diameter when I didn't have an axe handy. A couple of shots through each trunk and I was easily able to push them over with one hand.
It is worth noting that old 30-06 ball ammo and more modern 7.62x51 ammo would perform very similarly and be a big advantage against a threat hiding behind cover vs either 5.56 or 7.62x39.