I\'m looking for a simple clock synchronization protocol that would be easy to implement with small footprint and that would work also in the absence of internet connection,
Not really a proper answer, but just a reminder to make sure that you understand exactly what the hardware clock sources are and any caveats about them - especially if you are planning to use some slightly exotic possibilities like the low-power CPU / RTOS combination you mention.
Even the x86 case has at least 2 or 3 clocks which could be in use, depending on the setup - all with different properties.