Is there any way to hide your Steam status from others?

Solution 1:

Since a recent update, you can now set it so that only your friends, or no-one can see what you're playing.

Go to the Steam community settings page here, it can be found at that link or as this answer states, on Steam go to Profile > Edit Profile > My Privacy Settings > Game details
At Game Details you can choose between public, friends only or private.

This category includes the list of all games on your Steam account, games you’ve wishlisted, your achievements and your playtime. This setting also controls whether you’re seen as "in-game" and the title of the game you are playing.

Solution 2:

Open your friends list and change your status to Offline, and that should be what you need. You can't do it for specific friends, but if you're just trying to play solo that will do the trick.