Pigs naturally have somewhat dry skin. A healthy pig's skin (even though it is dry) does not usually bother him. He will occasionally rub against hard corners, etc. to scratch, but it shouldn't be something that consumes him and he should not look uncomfortable. If you find that your pig is scratching a lot, has redness or bumps or seems to be uncomfortable a lot of the time, there is probably something going on.
The most common skin problem I have seen in pigs is mange. Most of the pigs I have rescued have come with varying stages of mange...from mild to horrific. The symptoms of mange include 1)dry, scaly skin (with "dandruff") that often leaves a white track where the pig rubs against dark surfaces. 2)Tiny bumps and/or scabs just below the surface of the skin, usually behind ears, under front legs and chest, between back legs down to the hoof. The skin in these areas will take on an orange color. 3) Eyes develop an orange/brown crust in the corners and can begin to tear, leaving brown stains. 4) Ears have excessive brownish debris and can have an odor. 5) Excessive itching.
A pig can have all or some of these symptoms. Left untreated, this condition can become chronic and can lead to other health problems. It is very important to treat it at the first sign of a problem. I have seen pigs so infected that their hair and skin was literally falling off.
For my pigs (again...I am not a vet and always recommend speaking to your vet with any health concerns you have), I use Ivermectin for Cattle, Sheep and Swine. I give a TOUCH more than what the box says and I give it orally, spread evenly over their food. It's important if treating more than one pig at a time this way that you be sure they eat only their own food so they are getting the proper amount. I clean/wash all shelters and bedding areas thoroughly and then repeat the dosage in 14 days. Very severe cases may require a 3rd dose in another 14 days. This treatment has cleared up even the most severe case of mange we have seen.
I also routinely give my pigs the same '2 dose over 14 day' treatment of Ivermectin every spring and fall for worms and parasites. This has kept mange from being an ongoing problem with even the very severe cases we have encountered. Even though I am very against over medicating animals, I do recommend this for all pigs, regardless if they are showing symptoms or not. Because they are so susceptible to worms and parasites, preventative measures can nip the problems before they start.
There are other skin conditions that could be causing your pig's problems such as ringworm and other fungal issues. I have not personally encountered these issues with my pigs so don't feel confident talking about them, but they are something to speak to your vet about. A skin scraping is usually all it takes to diagnose the problem and the treatments are not usually difficult. Left untreated, they can lead to very painful open sores on your pet. Always be sure to take note of the condition of your pig's hair and skin daily and pay close attention to any changes. Even poor diet can cause skin conditions.
Often times a pig with a severe skin condition will look VERY bad. Some might even think it would be kind to put such an animal "out of it's misery," but I don't believe this is the case. With treatment, every pig I have seen has made a full recovery. I realize I have not seen every pig out there, but only after making every effort possible, will you truly be in a position to make a serious call like that. Treatment is often very simple and recovery in such a sad pig is always such a joy to watch.