http://www.ign.com/articles/2017/03/17/nintendo-switch-may-eventually-support-cloud-saves-after-all
Nintendo appears to have a cloud save system in place for Switch that only the company itself can access.
Reddit user Patsuann sent their Switch out to Nintendo for repairs, and upon receiving and booting up the console, they noticed that while their account was on the system, none of their game saves were stored on the system memory. However, on starting up The Legend of Zelda: Breath of the Wild, Patsuann noticed there was a small cloud icon next to the game.
The user was then prompted to download an update, and after the download was complete, all of the their saves were restored on the system. Patsuann uploaded footage of the process here, screenshots of which you can find above and below.
Nintendo has yet to announce plans to add support for cloud saves. It appears only Nintendo currently has the ability to freely transfer save data, and if players are to retrieve their game data in this manner, they'll have to be granted access by Nintendo.