when a Linode Dom0 is rebooted, how are the guests handled?

are they snapshotted, then restored to prior state? or, are they shutdown then rebooted?

a case example -- if my pygrub-booted DomU's running a given version of kernel, and i've upgraded to a newer kernel -- but not yet booted to it -- if Dom0 reboot occurs in this state, will my DomU come back up in 'old' or 'new' kernel?

My understanding is that they are shut down, then rebooted. I guess that means you'd boot into the new kernel.