much more likely to get a huge oak crashing down from lightning
You do have to be a little bit careful not so much about direct lightning strikes as earth potential differences between buildings when there's a lightning strike somewhere nearby. You've got (say) 30,000 amps entering the soil at one point and spreading out in all directions, giving a voltage gradient through the soil, so earth potential in different buildings will be different if they are different distances from the strike.
In my experience you are usually OK with UTP ethernet - the 1500V isolation in the interfaces at each PC is enough. Things that are earth-referenced (intercom systems, old-school coax ethernet, RS232 wiring etc.) can give big problems that are very difficult to protect against with surge suppressors and the like. Indeed, inappropriate use of surge suppressors can make things worse.