Yes, hang your tarp lower if you think you could get wind blown rain/snow.
I am also a big fan of the Warbonnet hammock sock when the weather could be cold/wet/windy.
I set it up ready to use when I hang my hammock, but roll it up and tie it along the ridgeline until I need it.
It helps add warmth, especially in wind, and helps keep spray, splash and snow from getting on you and your puffy layers. You pack up relatively dry gear which saves weight.
It also makes it so you can get by with a smaller/lighter tarp in adverse conditions.
No need to carry a heavier/bulky winter tarp and you can extend the temps of your insulation.
Your experience with a sock may be different than mine, but I consider it one of the best ways to reduce weight. 9 ounces for a Warbonnet Travel Sock saves more weight that you would have to carry with your additional insulation and tarp coverage for adverse weather.