when you kill a skeleton horse isn't the same you don't get the advancement "monster hunter" but you kill a zombie horse you can get it
normally this advancement can be achieved by killing the following mobs:
.Blue spider
.Spider
.Zombie Pigmen
.Enderman
.Polar bear
.Blaze
.Creeper
.Evoker
.Ghast
.Guardian
.Husk
.Magma Cube
.Shulker
.Silverfish
.Skeleton
.Slime
.Stray
.Vindicator
.Witch
.Wither skeleton
.Zombie
.Zombie Villager
moreover you can see in the screenshot n ° 1 the zombie horse is invisible and makes appear its shadow on the ground you will have more information on this issue MC-124147
the zombie horse isn't a hostile mobs.
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[Mod] FVbico (Steven Verbene) it doesn't prove that it is intented progress is achieved with only hostile or neutral creatures while the zombie horse is not hostile and they spawn in survival the creatures included in "Monster Hunter"
Intended for 2 reasons:
it’s not a hostile mob
it doesn’t spawn in survival.