A point will see United progress from Group A to the last 32, with a loss even enough should Feyenoord fail to win their match against Fenerbahce.
Zorya are already out of the competition but they restricted United to a 1-0 win at Old Trafford, playing on the kind of surface they can only dream of.
The Chornomorets Stadium pitch is frozen in places and patchy in others
United defender Daley Blind said it was "like a rock" when going out to train and the world's most expensive player Paul Pogba laughed, as did several others.
The players' studs clacked on a surface that faces a routine pitch inspection at 10am local time (8am GMT) and Jose Mourinho questioned why European governing body UEFA allows final group matches to be played in countries where winters hit so hard.
"The pitch is very hard, the pitch is very icy,'' the United boss said
"I think UEFA know the conditions of the pitch and everybody knows that in mid-December the conditions in Ukraine and Eastern Europe are more difficult.
"So if UEFA was worried about it, they should change the fixtures and not allow the last fixtures to be played in mid-December.
"If the fifth fixture is the last fixture here, it would be the end of November and not mid-December, so I think that's the problem.
"I think the stadium is beautiful, it's new, it's well taken care of.
"The pitch is the same
They are trying, they are putting some warmth on the top of it, but the pitch is very difficult and people cannot make miracles
Let's hope everything goes well."
One Zorya official was confident the match would go ahead, pointing to temperatures being forecast to rise above zero before the game and the ongoing work with heating on the pitch.
United trained on 70 per cent of the playing surface in temperatures that dipped to minus eight Celsius, having agreed the area in the shade of the stands would remain covered.
It is not the first time United have had problems with a pitch since Mourinho's arrival
In July, the Bird's Nest quagmire cost them a money-spinning pre-season friendly against Manchester City in Beijing.
Much more is at stake in Ukraine given progress is on the line in the Europa League - a competition that sees the winner through to the Champions League.
United are already nine points off the top four in the Premier League, meaning their prospects of reaching the Champions League that way already look slim, but Mourinho says that has not heightened the importance of this competition.
"No, we go in the same direction," the Portuguese manager said.
"We assumed from the beginning that it was an important competition for us - difficult because we play Thursdays and then we play Sundays.
"We are never given a Monday match to have one more day to rest and prepare, so it is difficult.
"It's a difficult competition to play together with the rest of the competitions.
"But we want to try to win it and while we are in the competition we try to win it.
"Today we are in the competition, tomorrow we want to win it and we want to go to the knockout (stage) and we want to try and go as far as possible, step by step.
"The first step is a difficult one, which is to qualify from a very difficult group."
Source : PA