If your gear is dripping wet, set-up your tarp to find a safe haven. Remove wet gear and wring it out, then put on on your best, and hopefully driest base layer. I'm hoping you have appropriate rain gear to avoid getting everything wet, but this could happen, so its a good scenario. A tipped canoe or slipping during a river crossing, etc.
Stay active to generate body heat. A dry bag or two for your clothes and sleep gear is highly recommended, for just such unforeseen scenarios. Eating a quick warm meal and warm drink does wonders for the body.
If you have a set of hiking poles, or find some suitable sticks, you could fashion up a clothesline to one side of your hammock. But if your wringing out the gear good, you should be able to go with the ridgeline.
My fleece and polypro clothes dry out really fast, so makes sure your choosing good clothing to carry. Stay away from cotton, it takes forever to dry and offers very little insulation value.