Cortana is essentially “hey google” or " Siri," but for windows.
When windows 10 is released at the end of July, initially you won’t be able to do anything directly with Cortana and SmartThings. Just like you can’t do anything directly with Siri and SmartThings.
Just like Siri, though, you could probably use Cortana to send an email to IFTTT and get indirect integration that way.
It’s Unlikely that it would ever be as good as Echo, because echo’s huge advantage is its hardware, which has amazing farfield recognition. If you’re running Cortana on a PC, you’re probably going to have to be sitting right in front of it in order for it to understand you.
since Smartthings doesn’t have A program that runs on your PC, you’re basically going to have to treat it like a cloud to cloud integration.
So could someone eventually write some software that would allow for integration between SmartThings and a PC running Cortana? Sure. Will it happen soon? Who knows, that would depend on community members. I don’t see it being an official integration anytime soon because of the hardware limitations.
Until someone writes some specific integration software, though, Just having Cortana on a PC won’t give you anything more than the option for an IFTTT recipe.