All six matches appear very unlikely to go ahead on Saturday, prompting Beattie to suggest a cessation to league rugby in the depths of winter.
"In Glasgow, practically nothing has moved for nearly a month," said Beattie. "At West we have not played for four weeks, yet we have had to keep training as best we can. We have snow forecast for tonight and a severe frost is continuing, so it looks as though our match against Melrose will be off. It's the same almost every year, though this year has been the worst I can remember.
"For two months every winter we ask amateur players to play and train in either mud or ice. It's just crazy. Clubs don't have undersoil heating or proper indoor facilities, so what do we do to try and keep players fit and interested? We should seriously consider taking a two-month break, and look at playing matches in late April and May and even into the summer months.
"I know there are clubs who depend on the facilities of fee-paying schools who might have difficulty using their pitches when cricket and athletics are scheduled, but surely some sort of sensible compromise could be found?
"If we knew we were going to play in April and May, we could then just plan for a winter break, tell the players to keep themselves fit at their local sports centres but enjoy the festive season with their families and mates."
As with West's Burnbrae, at the other Premier One grounds the picture is very bleak.
"It's only fit for ice hockey," said staff at Millbrae where second-placed Ayr faced a vital match with Dundee HSFP.
The match at ice-bound Philiphaugh between Selkirk and Stewart's-Melville FP could be called off as early as tonight. Selkirk president Donald Macleod said: "We will meet tonight and decide, but the forecast is for more of the same. The last thing we need is another fixture pile-up, as we have the Border League as well, but the reality is that if people had not been on holiday today, the decision to postpone would already have been taken."
Concern over fixture congestion is growing elsewhere. Heriot's match against Glasgow Hawks at Goldenacre "needs a miracle," said the home side's president Peter Brown, who added: "The backlog is building up already and we will have to see when the postponed matches can be played."
Malleny Park was hit by the blizzard which wreaked havoc on the west side of Edinburgh at the weekend. Currie are due to host local rivals Boroughmuir but assistant coach, Campbell Reynolds, said: "We have six inches of snow and the ground is frozen underneath. It's very unlikely that the game will go ahead."
Myreside is also under six inches of snow ahead of Edinburgh Accies' visit, according to Watsonians' president Brian Drinkwater who said: "Unless there's a thaw it will be very unlikely that we will be playing."
Even before the big freeze deepened, numerous Premier One matches had already fallen victim to the weather. Only the Melrose v Selkirk encounter, which finished in a 14-14 draw, survived the initial cold snap that claimed all the other Premier One fixtures on 18 and 19 December.
The Championship rules allow for up to seven stand-by dates which could extend the season into May, but the first three dates – 13 and 27 February and 20 March – are during the Six Nations and clubs may be faced with the prospect of morning matches or players being absent as those are the dates of Scotland's three away games in Cardiff, Rome and Dublin.
A spokesman for the SRU pointed out that if the cold snap continued, the Championship Committee could take "creative" decisions to ensure the league season was played in full.
On the question of a winter break, he said: "It is the clubs' championship, and if there is a consensus, the clubs could put a motion to the agm on the issue."