I thought that throwing a splash potion of Fire resistance at a normal burning Skeleton (because of daylight) would put out the fire (causing the sporadic one frame burning animations found in Pigmen & other mobs with natural fire resistance). It didn't. The Flaming Skeleton doesn't seem to be taking fire damage under the potion effects, however. It still thinks it's burning, and its AI doesn't shoot at my snow golems that are throwing snowballs at it.
It doesn't matter if the Fire resistance is applied before or after the Skeleton catches fire.
This is also true for Zombies (normal and villager), with the exception of the babies (which don't seem to burn without potions anyways.)
EDIT: works with any flammable mob that steps on a flaming block.
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What do Nether mobs have that keep the flames off them?
Either Nether mobs should burn like normal mobs (their strange burning has already been reported as a bug) or fire resistant overworld mobs should burn (if you call it that) like nether mobs.
The AI needs to be changed as well, because they're not REALLY burning.
(Also, Blah, I doubt that would work in the Nether. There should be a solution that works in every dimension.)
This is intended.
Fire Resistance will basically make it resistant to fire and lava. Although the mob will have flames, it won't take damage.
To extinguish, use water.