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.

The post on his Twitter account on Sunday night provoked an angry reaction on social media and was later deleted.
Mr Adams has said his use of the word was ironic and not intended to offend but admitted it was "inappropriate".
He added that attempts to suggest that he is racist are "without credibility".
The Sinn Féin leader's initial tweet appeared to compare the experience of a character in the film Django Unchained to the treatment of nationalists in Ballymurphy in west Belfast.
Speaking at a press conference at Connolly House in Belfast, he said: "I have acknowledged that the use of the N-word was inappropriate. That is why I deleted the tweet.
"I apologise for any offence caused."
Ten people were killed in Ballymurphy during a series of shootings by paratroopers in 1971.
Django Unchained is set before the American Civil War and focuses on racism, slavery, violence and murder.
Mr Adams said he is opposed to racism.
"I stand over the context and main point of my tweet, which were the parallels between people in struggle," he said.
"Like African Americans, Irish nationalists were denied basic rights.
"If anyone is genuinely offended by my use of the N-word, they misunderstand or misrepresent the context in which it was used.
"For this reason I deleted the tweets.
"I have long been inspired by Harriet Tubman, Fredrick Douglass, Rosa Parks, Martin Luther King and Malcolm X, who stood up for themselves and for justice."
Belfast man and former republican prisoner Tim Brannigan, who is of mixed race and who knows Mr Adams, said he was "shocked" that he had used the term.
"Gerry and Sinn Féin won't need me to tell them just how toxic it is and the sort of reactions it gets," he said.
"I don't think that you can equate what was happening in Belfast in 1965 with slavery.
"I posted about [US President Barack] Obama's speech to the White House correspondents' dinner, and his opening line was: 'There are some jokes white people can't make.'
"I think Gerry has been caught out by that."
Politicians from several rival parties have criticised Mr Adams' remarks on Twitter.
The DUP's Nelson McCausland said that having "compared himself to Rosa Parks only a few weeks ago Gerry Adams has now moved from the bizarre to the indefensible".
"That he would delete the tweet, then claim that his use of it was "ironic" before being forced to say it was "inappropriate" demonstrates very clearly the mess the  Sinn Féin president put himself in," he added.
Ulster Unionist Party (UUP) leader Mike Nesbitt said: "I find it extraordinary that the leader of a political party can even think to utter the words that he did."
He added: "To try to liken the fight against slavery to what was happening in Northern Ireland in the 1960s is contemptible."
SDLP leader Colum Eastwood said the tweet demonstrated "a staggering deficiency in judgment".
"Using the language of slave owners is never appropriate," he said.
"If a similar remark had been made by any other political leader on this island, Sinn Féin would have unleashed an orchestrated wave of angry condemnation."
Stewart Dickson of Alliance said: "Only a few weeks ago, Sinn Féin were comparing Mr Adams in all seriousness to civil rights hero Rosa Parks.
"This is proof, if it were ever needed, just how delusional that viewpoint is."
Jordan Armstrong from the Traditional Unionist Voice (TUV) party said it was "insulting to dismiss the suffering of the slaves in such a flippant manner".
He added: "In many countries, Adams's tweet would spell the end of a political career."
Barnet have signed winger Luke Coulson from National League side Eastleigh, with left-back Sam Muggleton moving in the opposite direction.
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Sinn Féin president Gerry Adams has apologised for using the 'N-word' in a tweet comparing the plight of slaves in the United States to the treatment of Irish nationalists.