Never tried the wrap approach.
For shorter local runs like the 4 mile one you describe, I typically don't bring any sort of rain protection. I just get wet and muddy and try not to stop and get cold. I don't like to carry anything with me on those shorter runs. I have some bike style shirts with rear pockets that I will occasionally put a wind shirt in if I plan on stopping, say above treeline for a rest or something. On longer intervals I wear a running pack to carry clothing, food, and water.
For longer (like day-long) adventures I usually will plan in advance and try to take advantage of nicer weather when I can. But that doesn't always work out. If it is almost guaranteed to rain I bring a hooded rain jacket with me. If the liklihood of rain is rather low, I might chance it with just a wind jacket, but I recently snagged a 6oz WPB hooded jacket that packs down to almost wind shirt size, so that would probably be my go-to choice for a potentially rainy day (forecast calls for 30-60% chance). For a higher probability of rain I will bring a heavier but more breathable jacket that works better on the move.
There are a lot of variables that will affect my decision, however. Temperature is a huge one. The above scenarios I'm probably looking at 50+ degrees. Below that, I'll be a lot more cautious on a long day far from shelter. Also if its very warm out and looks like just a passing storm, I'm usually fine with getting rained on, counting on being able to dry out after the storm passes. Usually these passing storms are a pleasant relief and very refreshing.
Take note that when I talk about wearing a jacket for a long day running adventure, I am typically moving much slower than my short run pace, so it's tolerable to wear a jacket on the move. I need to get better at proactively putting the jacket on though, to keep from getting rained on in the first place. It's nicer to NOT be wet all day if it's avoidable. I also don't usually stop for longer than a couple of minutes at a time, even for a 15 hour day. That can make a big difference for maintaining warmth while wet.
I tried and found I really don't like ponchos.
I almost never bring or wear rain pants unless I'm out for more than a day. I typically wear shorts with a boxer-brief liner built in. I'm usually comfortable enough even if they're soaking wet.