The following is a rather general and not very definite answer, but well, it isn't a particularly easy or clear-cut topic in the first place and I'll try to illuminate the subject from various angles.
First of all, of course I (and I suppose everyone reasonable) agree that "As a community, our aim should be to add more active and constructive users, not to deter them." I also agree that downvotes can have the effect of discouraging new users who might not be perfectly aware of how this site works and what downvotes actually mean. There is however a difficult balance to strike between voting responsibly and voting "friendly". Voting (no matter if up or down) is still our best and most important tool for quality measurement and control and to be used for exactly that purpose.
Downvotes are exactly there to signify that a post has significant problems. Of course they should be accompanied by constructive efforts for improving the post, like comments or even edits instead of the downvote. This is why they are revertible once the post has been edited. And I have seen (and myself taken part in) many instances of questions getting improved (either by the asker or the community) to a degree that does not require downvotes anymore or even encourages upvotes instead. Likewise I often see downvotes on e.g. bad ID questions accompanied by proper comments asking for improvements (and that is a question category where the original author is usually required for improving the question as people can't just edit those necessary details in themselves).
As bad as it may sound, but if a question has a score of -3 it, well, probably isn't a particularly good question and the downvotes say exactly that and nothing else. It does not mean the poster is an idiot or not welcome here. I do understand that it might come across to new users that way if they are not aware of the SE system. But as much as we might try to be a little more lenient with downvoting posts from new and promising users, understanding how downvotes work and that they are about the quality of the posts alone and not about the users is a fundamental step in understanding and getting used to how the site works at all. This doesn't mean we should smash the whole might of our downvotes at a new and possibly confused user, but utterly shielding them against the reality of voting does not do them a good service in understanding how the site works either (and neither does it to the site and its quality, of course).
As I said, it's a careful balance and the quality and possible improvement of the post always has to be kept in mind. We can't do much else than encourage users to vote responsibly and constructively, and usually they do.
In such situation wouldn't it be fair to simply close the question and inform the OP about why it was closed?
If it is an obviously off-topic (or otherwise inappropriate) question that ought be closed with certainty anyway, then sure, downvoting seems rather useless, especially if the question itself (apart from not fitting on this site) is not that bad at all. And in fact I for myself usually refrain from downvoting a clearly closable question (at least if it isn't a downright rant or totally unstructured and incomprehensible rubbish), since it is indeed useless.
One thing that has to be kept in mind, though, is that only closed questions that are "unanswered" (in SE sense) and have a score of 0 or lower are deleted automatically after 9 days. And if a question is 100% clearly invalid (not a question that has even a marginal chance of possibly getting improved/reopened one day), we do not want it to stick around so downvoting such a question into deletability is definitely useful as the question is bad for the site to stay around.
A last general remark to all users: As bad as a non-constructive downvote without comments that might repell users is, an upvote made for the wrong reasons is equally detrimental to the community as it encourages wrong behaviour (from the asker and everyone else seeing the votes on the question). And while the assessment of what makes a "good" question can be up to each user himself to some degree and you might very well employ a slightly lower standard for newer users, "sympathy upvotes" that are only made to welcome users and no other reason, or to counter "evil downvotes", are wrong. If you don't think a question is good (whatever personal measures of "good" you employ, maybe even ones that favour good questions from new users), then you should not upvote it and doing so is against the workings and whole philosophy of SE. In the same way that votes are not to be used for punishing users, using them to give new users a "welcome present" is equally wrong. And neither are votes there for you to counter/invalidate someone else's right to vote (no matter if up or down) if only based on the assumption that this user voted for "invalid" reasons. An upvote does not say
Hi and welcome, you're a great person, and would you please please stay here?
This is a good question and exemplary for the content we want to see here. More of this please!
And this is the way in which we want to encourage constructive users to stay contributing.