Livingston FC are one of many clubs whose clearing efforts have been in vain
Only six of the weekend's 16 Scottish Cup ties have survived the freezing temperatures across the country so far.
Dunfermline's East End Park passed a Saturday morning pitch inspection ahead of Stenhousemuir's visit.
And police are happy with the area around Pittodrie, so Aberdeen's game at home to Hearts will go ahead.
Hibernian v Irvine Meadow, St Mirren's tie against Alloa and Sunday's match at New Douglas Park between Rangers and Hamilton have also beaten the freeze.
Thursday pitch inspections ruled out the fourth-round ties being hosted by Albion Rovers, Ayr, Edinburgh City, Forfar, Raith Rovers and Ross County.
Road conditions put paid to games at Inverness and Livingston.
Kilmarnock's game was also postponed because of police concerns on Wednesday, while Morton versus Celtic went off because of a frozen pitch.
More ties could be disrupted as the icy weather threatens to wipe out the weekend card.
A Scottish Football Association spokesman said: "Due to the extreme weather conditions, we have been proactive in encouraging early pitch inspections.
"Clubs are also advised to liaise with local authorities with regard to the surrounding areas of their grounds."
The SFA will give clubs as long as it can but promises there will be no repeat of the late postponement at Falkirk last weekend.
"Under the Scottish FA cup competition rules, pitch inspections can be carried out no later that four hours prior to kick-off but given the weather forecast for the week ahead, it is prudent for inspections to be carried out as quickly as possible," said the spokesman.
The forecast is for the freezing weather to continue into the weekend, making it almost impossible for clubs with no undersoil heating to make their pitches playable.
Morton manager James Grady said the postponement was the right decision but conceded his players were disappointed to miss Saturday's game against Celtic.
"We're disappointed as all the boys were looking forward to it," he told BBC Scotland.
"There'll be a lot more games than just ours put off this weekend so we shouldn't feel too hard done by."
Treacherous conditions mean there is also no guarantee that cup games at Scottish Premier League grounds will go ahead.
Despite the pitches being playable, SPL games have been called off because of police concerns about public safety.
Kilmarnock said in a statement that it would meet police to assess the possibility of the tie being played on 12 January.
"Despite the pitch being in a playable condition, surrounding roads and pavements have been deemed a risk to spectators," the club said.
"With ongoing low temperatures forecast and the possibility of further snowfalls, the decision has been taken to postpone the match at an early date in order to reduce inconvenience to supporters of both clubs."
The Scottish Football League has postponed Saturday's matches at Cowdenbeath, Berwick Rangers and East Stirlingshire, and a pitch inspection is planned on Friday at 1130 GMT at Balmoor for Peterhead's game with Clyde.
Unless there is a surprise thaw, it will be the third week in a row that Scottish football has been almost wiped out by the wintry weather.
With Scottish football being hit hard during the coldest winter for 25 years, lower league clubs are to share £1.5m to help ease the financial strain caused by the continued calls-offs.
SFA chief executive Gordon Smith said: "I must emphasise that this is a discretionary payment and is made on a one-off basis taking account of the financial position this year."
Clubs in the South and East of Scotland league will receive £7,500 each, with senior sides getting more.
Meanwhile, Ayr's Monday race meeting has also been cancelled.
Active Nation Scottish Cup fixtures
Saturday 9 January
Aberdeen v Hearts Albion Rovers v Stirling Albion OFF Ayr United v Brechin City OFF Dunfermline Athletic v Stenhousemuir Edinburgh City v Montrose OFF Forfar Athletic v St Johnstone OFF Hibernian v Irvine Meadow Inverness CT v Motherwell OFF Kilmarnock v Falkirk OFF Livingston v Dundee OFF Morton v Celtic OFF Partick Thistle v Dundee United Raith Rovers v Airdrie Utd OFF Ross County v Inverurie Locos OFF St Mirren v Alloa Athletic
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.