I want to keep my window open because it’s my preference. My landlord wants to keep it closed because they remotely controls the house’s A/C. They’ll walk right up to my room and slam it shut whenever they visits on random days to harass us about the kitchen looking like people live here.
You need to check on tenancy laws in your location.
It might not be considered trespassing, but it could be something else.
Here in the UK tenants have a right to “quiet enjoyment” as it is phrased in law, which means your landlord is not allowed to bother you unannounced, and if they want to come to the property they must give reasonable advance notice (usually 24 hours)
You may have something similar.
Then again, the landlord having remote-control over your A/C sounds like absolutely psycho behaviour already, so good luck with that.