Can I say "Is the air conditioning okay?" when I want to know if the a/c is cold enough for you?
Can I say "Is the air conditioning okay?" when I want to know if the a/c is cold enough for you? Or when I say so, a native speaker of English will intuitively assume that I'm talking about the quality or technology of the a/c.

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Perfectly acceptable, if you wanted to be really sure you could ask "is the Air Conditioning (A/C) ok for you?"

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Yes. It's not formal, but you can definitely use it. I ask my friends that a lot :)

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"How is the room temperature for you?" is what I would say.

"Is the air conditioning okay?" is what the Technical Manager asks a technician when he inspects a venue (before a meeting or a conference).