can you install zwift on smart tv

No, PC or MAC and soon iOS.

iOS now -> https://itunes.apple.com/nl/app/zwift/id1134655040?mt=8

No, but there is work underway for it to run on the AppleTV, which is a sort of third party tool to give smart TV functions to any display.

Has anyone heard about plans to make it work with Roku as well?