Is it perfectly natural to ask someone what is your mood? when someone wants to know how the person is feeling. If it is not natural at all, as I suspect, then what would they ask instead?
It is not natural to ask "What is your mood?".
A neutral way to ask is: How are you feeling?
To confirm that someone is happy: Are you feeling happy/good?
If you suspect that a person might not be well or happy: Are you feeling okay?
Or just: Are you okay/alright?
The latter are most common as a way of checking whether someone who looks ill is okay - or whether someone is injured after falling or being involved in a minor accident.
There are two possible questions here, namely Is this idiomatic English? or Is the question likely to be asked in a certain context (by a reasonable native speaker)?
Which are you asking?
Anyhow you can sidestep either question by rewording the specimen as a request.
Tell me about your mood, if you would.
One problem is that asking questions of the form “What is x?” can be interpreted as asking for definitions.
The habitual aspect may be expressed by an unmarked, non-progressive form.
To avoid such interpretations and others perhaps, one may use How is x +
expression of time.
The indication of time isn’t necessary, but it can help to make the sense clearer.