Former Manchester City trainee Coulson, 22, joined Eastleigh from Oxford City in January 2016 and has scored six goals this season.
Muggleton, 21, moved to Barnet in 2014 and helped them win promotion back to the Football League two years ago.
Both players' moves are for undisclosed fees.
Find all the latest football transfers on our dedicated page or visit our Premier League tracker here.
Barnet have signed winger Luke Coulson from National League side Eastleigh, with left-back Sam Muggleton moving in the opposite direction.