All right, so I found this out after looking through the issues backlog on github for Visual Studio Code. You can set word wrap for markdown, but you have to do it specifically for markdown, because apparently there's some kind of default overriding here.

Use Ctrl + Shift + P to open the command palette, then type in settings. You're probably just interested in Workspace Settings.

Screen-Shot-2018-04-27-at-3.34.28-PM

You'll get something that looks a little bit like this. But only a little bit. I've already put in some settings.

Screen-Shot-2018-04-27-at-3.35.31-PM

The significant part here is that last element:

{
    "editor.wordWrap": "wordWrapColumn",
    "editor.wordWrapColumn": 80,
    "editor.wordBasedSuggestions": false,
    "[markdown]":{
        "editor.wordWrap": "wordWrapColumn",
        "editor.wordWrapColumn": 80,
    },
}

...the one that starts with "[markdown]". I have left in the other word wrap stuff in order to continue keeping my text files at 80 characters, but the default settings for markdown override those settings. In order to prevent that, I have copied that stuff into the markdown-specific section.

Again, the reason for setting an explicit wrapping column of 80 is to keep my lines exactly the same length in terms of characters/words/etc. This is done in order to help me to develop a "feel" for the length of a paragraph or, you know. Whatever.