(1) Would you mind if I smoked here?
Is (1) a conditional (i.e., a sentence containing a conditional clause)?
Or is the if-clause complement of the verb mind?
I feel the need to make it clear that the intended context for the OP is what you normally would expect, i.e., a question coming from a smoker who'd like to smoke at the time of speaking. Somehow I feel that this type of question is not to be lumped together with a hypothetical question where the speaker does not necessarily intend to smoke at the time of speaking.