I wish running Zeppelin on windows wasn't as hard as it is. Things go haiwire if you already have Spark installed on your computer. Zeppelin's embedded Spark interpreter does not work nicely with existing Spark and you may need to perform below steps (hacks!) to make it work. I am hoping that these will be fixed in newer Zeppelin versions.
If you try to run Zeppelin after extracting the package, you might encounter "The filename, directory name, or volume label syntax is incorrect."
Google search landed me to https://issues.apache.org/jira/browse/ZEPPELIN-1584, this link was helpful but wasn't enough to get Zeppelin working.
Below is what I had to do to make it work on my Windows 10 computer.