It's a lovely warm sandstone. We don't know very much about how gates were hung in the past - the best way is to look at old paintings. The pierced stone has clearly been dressed on the upper cusp and this suggests that it is probably fairly recent. It's not the kind of place to put a gate though.
The stone across the stream is just as interesting and is probably worth checking to see if there is any trace of a soil line at either of the ends. The tall stone wall in the background is very neat ...