The easiest way would be to do the apt-get thing (not the zip thing). In this way, you will be able to upgrade your snapshot as you used to (apt-get update, apt-get upgrade)
To move from stable to snap, follow the installation instructions of the apt-get snap release.
Basically, 3 steps:
change your /etc/apt/sources.list.d/openhab2/list entry to use the unstable repository (remember to delete or comment out the existing stable repository entry)
apt-get update
apt-get install openhab2
The install command will effectively deploy OH2 snap on top of your existing OH2 stable (assuming that stable was originally installed used the apt method)