My guess is that Treyarch will release the tools at the end of the DLC season, possibly around September time.

They want to grow zombies and with a potential 3 year cycle coming up again, it's going to be a long time before Black Ops 4 or whatever comes next. Although the maps would be free per say, imagine the number of additional PC sales for Black Ops 3? Want to play Custom Zombies for Black Ops 3? Then get yourself a decent PC with the PC version of the game because the tools won't be coming to Xbox One nor PS4. Of course, DLC makes money so why let modders create maps for free? So why are they changing their mind now with Black Ops 3? I suspect it's the 3 year cycle. We all asked but at the same time we suspected that Activision wanted to keep modders away from Black Ops. 7 years ago the original WaW mod tools were given to the community but ever since then there's been a complete drought on any modding tools from Treyarch. Download the tools to create your own custom zombies maps or mods, or download other people's custom maps through the Steam 'Community' area.

Update Oct 2016: Mod tools have now been released (open to everyone). Starting with an early Alpha in March 2016, the zombies community will be able to test the new modding tools before their final release. I'm scrubbing my eyes with disbelief - Treyarch (and implicitly Activision) have just announced that Custom Zombies mod tools will be available for Black Ops 3.

Black ops 3 custom zombies