Aberdeen's surface is the worst in the Scottish Premier League with rugby and football internationals both adding to the wear and tear in recent months.
Smith knows they will have to approach Friday night's SPL clash differently, but he has not been able to put many plans into practice.
Smith, who has doubts over two unnamed players, said: "Both teams are playing on the same pitch so it's not a great issue.
"The boys know it's going to a tricky pitch to play on. We might have to adapt a wee bit.
"Because of the snow we have not really been able to do our normal training week.
"The players know what to expect and they know what I expect of them in the conditions.
"We try to get the ball down and play. We have to adapt, it's not always on, but when we can we will try and play."
Dundee fell 15 points adrift last weekend but Smith feels there is enough fight in his team to ensure they will never give up.
Smith's managerial career started when Dundee were plunged into administration in October 2010 and deducted 25 points, but he led his side to sixth place in the Irn-Bru First Division.
And he sees similar qualities in the character of his current squad.
Smith, who has been impressed with an unnamed striker during a trial spell this week, said: "Obviously the administration there was a great team spirit but equally, for different reasons, this is a strong dressing room.
"I know they will keep fighting, and that's the most important thing.
"They are not going to stop working as hard as they do."
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