The game was due to be played on December 19 but was frozen off and reports on some club websites this week that the rearranged fixture was already postponed have proved wide of the mark.
The weather is still a threat, but Heath coach Kevin Plant is hoping that the contest goes ahead at the start of an important spell for the North Dean side.
He said: "It is not ideal to have a game so early in the new year but it is the same for everybody.
"We need to get off to a good start in 2010 and set a marker down."
Plant added that January was a key month for Heath with fixtures against four of the top six - York, Castleford, leaders Wheatley Hills and Bradford Salem - plus a trip to Dinnington.
Heath are eighth with seven wins and seven defeats and the next month is likely to determine if they can go close to matching last season's fourth place finish or whether they might be casting a few anxious looks over their shoulder in the closing games.
Plant's side are yet to break their away duck this season but York have been hit by injuries and lost their last three games, by 28-3 at Scarborough, 14-3 at home to Keighley and 42-7 at Sheffield in their most recent game on December 12.
Heath were beating Skipton 19-16 at home on the same day, having previously lost 22-19 at home to Yarnbury and 36-17 at Sheffield.
The first meeting between Saturday's combatants resulted in a 23-16 win for Heath and Plant would dearly like to complete a double over a side coached by Ken Higgins, who Plant has worked alongside at Morley and Wheatley Hills.
Heath make changes with centre Jarrod Morris, blind side flanker Chris Haigh and No 8 or lock Ian Spence all unavailable.
Prop James Watson returns while No 8 Ian Downsborough and winger Matt Baxendale should have recovered from injury.
Plant, meanwhile, is keen to keep the Yorkshire Shield first round game against Huddersfield YMCA as a first team game. He says he would be happy to play it at Laund Hill under floodlights in midweek if necessary. The game was originally scheduled for November 21 and would have been played this Saturday had there not been league games to rearrange.

OLD Brodleians have a second team game at home to Harrogate on Saturday (2.15) but have named a powerful side as they build towards the first team contest at Morpeth in North One East the following weekend.
Lack of match fitness is a worry for coaches Ian Armitage and John Cole as Brods haven't played since the win at Ilkley on December 12, so they have named a side with plenty of first teamers.
One absentee is hooker Ben Morrell, selected for a Yorkshire under 20 squad game at Rotherham on Sunday, so Brods experiment with Keiran Nalton in the number two jersey.
Andy Finn and Jack Moon are back from playing with Leeds Carnegie's under 20 side while long-serving fullback Adam Standeven makes his return after an eight month absence during which he has had another knee operation. Centre Andy Clay also reappears after work commitments, on the bench.
BRODS: McLaughlin, Nalton, A. Skinner, Willis, Hanson, Finn, Steve Shaw, Akroyd, Gardiner, Holborough, Fowler, Hotham, Scott, A. Standeven, Moon. Replacements: Donlan, Millward, Clay, R. Cole.
The club's development side travel to Barnsley.

OLD Rishworthians' Andrew Curwell Celebration Cup match, postponed from last Sunday due to snow and ice on the Copley pitch, has been rearranged for Saturday (2.0).