As far as functionality goes, Windows 10 Cloud is similar to Windows RT, in that it can only run apps that are built for the Windows Store. While Microsoft hasn't actually announced this new SKU of the OS, a build did leak last week.
Twitter user Longhorn claims to have actually gotten Google Chrome to work on the OS, by turning it into a Store app via the Desktop App Converter.
Interestingly, while screenshots of Windows 10 Cloud build 15019 showed converted Win32 apps working, they did not work in the leaked build 15025. Fortunately, Longhorn has actually written a bit about how Win32 apps are blocked and how he bypassed it.
According to him, Windows 10 Cloud uses a "strongly enforced UMCI to make unsigned applications not work." Some of these restrictions can be worked around by using the Windows Subsystem for Linux, which inexplicably still works.
It would seem that Microsoft's plan is to license Windows 10 Cloud for free, as users will have the option to upgrade it to a Pro version of the OS. Even if it's still relatively easy to jailbreak Windows 10 Cloud when it finally ships, it would seem that a paid upgrade would still be the path to Win32 for most "normal users".