I think so, but most Eventers tend to stay Irish as there is a greater chance of getting on the teams etc.
NI is part of the UK
"great Britain" is technically just the isle - scotland, england and wales. but as it is "great britain and Northern ireland" then we are part of you lot, even if we do not come under great britain
lol its all very confusing if you dont live here lol
but best not to start an arguement over whether NI belongs to Britain or Ireland...