Steam Sucks, only losers use it. You cannot download missions from steam workshit unless you subscribe, ie register and login there. Stupid as hell to download simple mission. You could try to use http://steamworkshopdownloader.com but its not guaranteed to work on every download.
When you subscribe to a mission, steam client / ArmA 3(?) creates SteamPreviewCache\ directory in your profiles dir, it places preview image of the mission there (assuming, if one is available).
At in-game arma3 the mission is available from Scenarios → Subscriptions. When you select the mission there and click PLAY, then the mission is downloaded.
At hard disk the mission is placed in your profiles \Users\YOURNAME\Saved\steam\ directory.
Do not upload your missions to steam workshop, only release missions properly like we have always done.