Is there a way to hide a user's home folder from other users seeing that it even exists?

I want to hide a user folder from any other users from seeing. The user should still be able to log in through the login window using their username and password.

Is this possible?

You have two options. The first is to use Terminal to set the folder's hidden flag. Open Terminal from /Applications/Utilities and type the following command:

chflags hidden /Users/SHORTNAME

where SHORTNAME is the name of the user's home folder. This will hide the folder from Finder, but other users could still find it, or change Finder's preferences to show hidden folders.

Alternatively, you could place the home folder for that user in a different location. Open the Users & Groups (or Accounts) pane in System Preferences, click the lock to unlock it, right-click on the user, and choose Advanced Preferences…. Then click the Choose button after Home directory and find a different location (you might want to press Shift+Command+. to show hidden folders for this). Now, the user's home will be in a different place so others will have a harder time finding it.