Goals from Matt Brown and Tom Peers bookended a disappointing game as the visitors secured only their fourth away win of the season, condemning Halifax to just their third home league defeat.
Around 180 cubic metres of snow were cleared from the pitch by dozens of volunteers to ensure the game went ahead despite protestations from the Chester camp about the state of the penalty area in front of the South Stand.
Halifax were caught cold by a quick free-kick and from Sean McConville’s excellent cross, Matt Brown stooped to nod past Matt Glennon from six yards out.
James Bolton’s stunning volley just before the break was as close as the hosts went to scoring as it flew inches over.
So, too, did Craig Hobson’s acrobatic effort even closer to the interval after a Chester free-kick, and Halifax were looking uncharacteristically vulnerable from set-pieces.
Glennon then pulled a save right out of the top drawer from a rasping shot by McConville 25 yards out before Halifax cleared Ben Hennigan’s header off the line from the resulting corner.
The hosts went close when Bolton’s shot was well saved by Worsnop and closer still when Boden hit a post after inadvertently heading onto his shoulder.
They proved costly misses when Chester almost immediately broke away and sealed the win when substitute Tom Peers nodded in Jamie Menagh’s cross.
FC Halifax Town: Glennon, K Roberts, Bolton, M Roberts, McManus, Smith (Peniket 46), Maynard, Schofield, Hatfield (Pearson 71), Jackson (Marshall 51), Boden. Unused substitutes: Senior, Williams.
Chester City: Worsnop, Hennigan, Touray, Brown, Charnock, Menagh, James, Hobson (Peers 67), Rooney, McConville, Richards (Mahon 81). Unused substitutes: Roberts, Kay, Riley.
Referee: J Brooks (Leicestershire).
Man of the match: Danny Schofield.