What you describe sounds like what is called “paper skin,” and the wounds are “skin tears.” It occurs when you lose a few of the layers of protective fat that we all have under our skin. These layers serve as insulation and help to store oils which keep the skin supple, and water for general hydration. When you get older, over sixty say, you begin losing some of this fat and your skin becomes dryer and more fragile, you don’t store water as efficiently and require more frequent hydration, don’t tolerate cold weather as well, and are easily subjected to skin tears. This condition happens naturally with age, much earlier in smokers and people who are exposed to the sun for many years and is exacerbated by cold, dry weather, exposure to sun, and cigarette smoking. Some meds, such as the new blood thinner Effient (prasugrel) cause paper skin.
Clean skin tears by patting with clean moist gauze or cloth, or hold under cool running water, pat dry, apply thin layer of triple antibiotic ointment, leave open to air or cover with a synthetic skin product available at most drugstores that is recommended for covering these tears as the removal of tape or bandaids can cause the skin to tear further.
Hydrate and moisterize frequently and be more careful about bumping into things.