Skills aren't tied to classes. Just because a Cleric casts spells based on Wisdom, doesn't mean that Religion checks should also be wisdom.
By this logic, Arcana should simultaneously be an Intelligence (Wizard) and a Charisma (Warlock) skill.
According to the rules, a nature check "measures your ability to recall lore about terrain, plants and animals, the weather, and natural cycles." Sounds intelligence-based to me: memory and knowledge are definitely intelligence related.
That said, there is an optional 5e Rule Variant: Skills with Different Abilities. This allows you to use any ability score with any skill, assuming of course you can make a valid argument. In this case,
-Intimidation (Cha), for example, would be casually-but-menacingly explaining that "all sorts of bad things could happen to people that don't help us"
-Intimidation (Str) would be cracking your knuckles and generally being visually threatening
-Nature (Int) could be using your knowledge about different plants to identify a new plant and its effects
-Nature (Wis) could be noticing that the forest went silent, and using that perception to intuit a dangerous enemy nearby. Although this would arguably fall better under the Survival skill.
