Treating Wounds

The treating of wounds, from minor bumps and scratches, to potentially lethal breaks or gashes, can be viewed upon similarly. Mechanically speaking, the ability to treat wounds is tied to a medicine check, and the DC is based on the severity of the wound (determined by DM).
A small bump, scratch or bruise does not require a check at all. A below-skin-level slash, deep bruise, or minor fracturing of bones could be treated with around a DC 10 Medicine check. A heavy gash, stab wound, or shattered or broken bone probably requires around a DC 15-17 Medicine check. A likely-lethal wound, such as being impaled, having a limb severed, or any other similarly deadly attack, would require at least a DC 20. Of course, this all depends on the situation, and is up to the judgement of the DM. A smart player, (or a smart character, depending on their background) with knowledge on real life treatments could take necessary action and argue for a lower DC on these checks. Unless you're a doctor, you as the DM probably aren't aware on the best methods of treating fireball-inflicted third degree burns, so use your best judgement.
The important thing about this, is that any wound that would have a DC 12 or above Medicine check is a wound that would in some way inhibit regaining full health with a long rest. If you feel as if the injury could not be healed properly by just laying down and sleeping for the night, the DC should be at LEAST 12. If you feel as though the injury is mostly just pain in a certain location, or a scratch wound that could easily be forgotten about or ignored with a full night's rest, then the DC would be under 12. Again, use your best judgement.
Willpower, as stated in another article, could be used to overcome the injuries that might inhibit certain movements or actions, but to be used with caution. As we all know, pain is a very necessary thing, and ignoring pain and fighting through it often isn't worth the price you pay for it.