Only two Scottish League grounds - Ibrox and Tannadice, which both have undersoil heating - were able to stage matches on Boxing Day, and the situation on Saturday looks likely to be the same.
Rangers are due to entertain Hibernian in the only Premier Division match with any realistic chance of being staged, while Dundee United are scheduled to meet Airdrie in the First Division.
There was a gloomy outlook elsewhere. Gerry Collins, the Falkirk assistant manager, ruled out his club's Premier Division fixture against Motherwell. "There is no chance [of playing the game] unless there is a dramatic change in the weather," Collins said. "We have covers on the pitch and snow on top, but the ground is bone-hard."
At Tynecastle, where Hearts were hoping to entertain Celtic, the chairman, Chris Robinson, said: "The pitch is covered but is hard, and there's no real chance of the game being on. We will confirm on Friday whether it can go ahead or not."
The match's postponement will mean the Edinburgh club going nearly six weeks without any gate receipts, with their last home game staged on 2 December. The next Tynecastle match is likely to be the rescheduled Motherwell fixture on 10 January.
Robinson, whose club are reported to be struggling financially, added: "The lack of funds will be a big strain and we stand to lose up to pounds 30,000 if Saturday's game is postponed. But we have to manage our finances and get on with it."
If the match is postponed it will give Celtic selection problems for the "Old Firm" game against Rangers on 3 January. John Hughes and Peter Grant will both miss the Parkhead encounter: each player has one more game to sit out as part of their three-match suspensions.
Kilmarnock are hoping the use of hot air covers can clear Rugby Park for Saturday's visit of Aberdeen.
A Scottish Football League spokesman, Hamish Walker, said there were few expectations that the cold snap will force a major fixture backlog. Walker said: "We have already rescheduled games for January 9, 10, 16 and 17 and, while postponements obviously cause headaches, there are not too many midweek matches scheduled over the next few months."Reuse content