I had an issue with this as I just started a server for me and my friends the other day. Basically the steam workshop directory is different than that of the one the server uses when you run it. I'll do my best to walk you through what worked for me.
Go to your steam directory and go to your workshop folder, then continue to content and then 108600 (This is the PZ content):
Yourdrive:\Steam\steamapps\workshop\content\108600
Now you are going to see a bunch of folders with numbers, each number represents a different mod by ID. Clicking on a folder will open up to a 'mods' folder, do into that will present you with a folder with the name of that mod. Here is an example for a mod I have
Yourdrive:\Steam\steamapps\workshop\content\108600\532252577\mods
You're going to want to copy the folder that has the name of the mod, and all of the contents with it. Now in another window, go to the following directory: Yourdrive:\Users\YouUser\Zomboid\mods
From here you will want to paste that folder you copied into the 'mods' folder located in the Zomboid directory. This is the location from which your server is running its mods from from what I understand. Now you will have to do this for each mod that you want to run on the server. After doing this you can delete the mods from the steam workshop directory if you want. If not, you will just have each mod listed twice in the games interface when selecting what mods to enable. Have them both enabled doesn't seem to have any negative impact for me on my sever so I just left them in there. Hope this helps.
The only thing I couldn't seem to figure out was how to get my server to prompt people for a download on the files that they don't have to play on the server. As a result I have had to just send my friends all the mods I am using so they can download them themselves prior to joining the server.