One if the biggest things to remember is that down voting is only seen as a negative thing.
There have been many posts discussing this already, across lots of the stacks sites, about dealing with the "negative impact" of downvoting on new posts, as well as potential "fixes" such as forcing a comment to explain why you downvoted.
However, none of that is really necessary, as the system is purely logical, and there is plenty of explanation to go along with how the system works. The downvote button even has a tooltip:
Poor quality or not useful.
This is pretty self explanatory. If a post gets downvoted, especially a post by a new user, they're being told that their post isn't useful, or is pretty poor quality. We can then help further by leaving a comment, explaining exactly how they can improve it, but again, these comments are often paraphrasing the "How to ask" section of the site tour.
That said, yeah, it's always a bit of a kick in the gut when you get a downvote. We're only human. But after all I've already mentioned, the system is in place to incentivize users to improve and do better; and when/if they do, downvotes can be retracted, and even changed to upvotes. Removing that functionality to protect their pride completely goes against its intended purpose.
As for "protecting new users", well, unfortunately that opens up a lot more problems. Firstly, what determines a "new user"? Number of posts? Time on the site? Reputation? These things can be used to determine a "new user", but it's not overly definitive. There's always going to be people who slip through by not being overly active, have a few posts that have all received votes, both up and down, keeping them in that low threshold, but still have been a member for at least a year. The logic is not really something that can be defined.
And ultimately, changing user privilege is a system-wide thing, not just relevant to us.