Sharing VirtualBox snapshots
Solution 1:
Yes you can. I send vbox snapshots between a laptop and desktop frequently. First you make the snapshot current and then export the entire VM as an appliance.
Solution 2:
It should be possible to just send the ".vmdk" and ".sav" files that you can find in the Snapshots folder.
However, just copying these files will not make it appear in the VirtualBox GUI. For that, you will also need to edit the ".vbox" file that has all the information about which virtual harddrives belong to which VM's and so on.
Instead of editing your ".vbox" file, the easiest solution would probably be to copy the whole Virtual Machine folder except the really big ".vmdk" file that represents the baseline virtual harddrive. And then plug in this file that you have locally on your machine, anyway.
Solution 3:
Even Exporting the whole appliance in *.OVA file will not save your snapshots tree, You will et the whole disk overlayed with the latest snapshot the machine was using before exporting.