Does a minor software update effect rooting method? I'm a newcomer to Android, so I'm not very familiar with how rooting works on Android. In IOS minor updates such as going from 9.0 to 9.1 can sometimes result in a jailbreak method not working, I was wondering would that be the same if a Samsung S7 edge is updated with a minor security update from Samsung.
This ultimately depends on the manufacturer. Samsung is not at all friendly to the rooting of it's stock ROMs, and does lots of modification to it's Android ROMs, so I'd say it is a real possibility. If it were me, I would install Cynaogenmod instead if I were to root but still wanted OTA updates.

Google itself, which is where the baseline Android comes from, usually doesn't care all that much if people want to root their devices, and usually doesn't plug holes that allow rooting unless customer data is at risk as a result.