The gate at https://www.openstreetmap.org/node/10886350135 has a sign saying "private" on it, but in this edit I've not added explicit access tags to https://www.openstreetmap.org/way/1168918378 .  I've added "motor_vehicle=private" to https://www.openstreetmap.org/way/1171570694 based on the sign at the north.
I have not (yet) set foot, bicycle or horse access tags.  
Generally speaking in Scotland, https://www.outdooraccess-scotland.scot/ should apply.  See https://www.outdooraccess-scotland.scot/sites/default/files/2018-05/Publication%202005%20-%20Scottish%20Outdoor%20Access%20Code.pdf for an English PDF version.