Ok, so I was having trouble with wine -- it was starting up slow, and I decided I just wanted to delete everything in it and start over. After a while, I figured out how to do that, and I'm posting this here in case anyone else needs to do the same. Hopefully, someone will find this useful.
To reinstall wine, run:
sudo apt-get remove --purge wine wine1.2 winetricks -y -f
rm -rf $HOME/.wine
rm -rf $HOME/.winetrickscache
rm -f $HOME/.config/menus/applications-merged/wine*
rm -rf $HOME/.local/share/applications/wine
rm -f $HOME/.local/share/desktop-directories/wine*
rm -f $HOME/.local/share/icons/????_*.xpm
This will delete EVERYTHING in your Wine installation. Make sure you don't have anything you care about in there before doing this.
sudo apt-get install wine1.2