"I… would like to give my students feedback on their initial posts. Do you know how I can set it up so that I can interact with the students about their posts in a private way?"
I knew there was a way to enable private replies in a Moodle forum, and I found it.
NOTE: This feature is only available in the Advanced Forum, and not in the "standard" Moodle Forum.
Navigate to the Advanced Forum settings, and look for the "Post options" section. Check the "Allow private replies" checkbox, and then save your changes at the bottom:
When you want to make a private reply to a forum post, be sure to click the "Private reply" checkbox at the bottom right:
And that's all there is to it!