I saw loads of Loblolly for posts and beams -- it's a real good structural lumber (one of the SYP species prized for framing lumber) however it will wander if you don't saw it properly and stack/dry it properly. That said, I have great luck framing with green lumber since I can get it up and pinned into place before the wood can wander.
SYP loses quite a bit of moisture and weight within 2-3 weeks at average humidity. I've seen it get down to 25% moisture content after just 3 weeks at 57% humidity in my storage area where I run a dehumidifier.
I have never sawn 4x4 but do lots of 6x6 and larger posts, and various size beams. I tend to reserve smaller trees for posts, or the tops of bigger trees. It means I can make a nice post with the heartwood centered and not have much waste. The larger logs go to better uses such as boards or 2x lumber, but you can certainly plan things to slice off some nice lumber and save the core of the big log for a post.
You may want to setup a toeboard if you don't have one already, as it will help keeping the heartwood centered when the log is tapered. This will greatly improve the yield and quality when sawing posts, especially when using smaller logs. For a dimensional 4x4 (3.5x3.5) you just need a 5" log if you don't mind eased corners.
Unless there is a reason you want 4x4 specifically, consider going up a little in size. It will be more stable and it will probably look better too. A 4x4 can be awful spindly looking as a deck post.