Estate agents say there are no signs the economy has picked up enough to fuel a widespread rise in prices, and have called on lending companies to ease their grip on the purse strings so cash can be injected into the market.
However, they said people who were prepared to sell at realistic prices would continue to find buyers and that demand for some types of properties will be high.
In a year of fluctuating conditions, house prices fell overall in 2012, with the average price dropping by more than £5000 to £142,246 from £147,494 in November 2011.
Michael Luck, managing director of Slater Hogg & Howison, believes the market will see little growth in the coming 12 months. He said: "I think house prices will remain stable during 2013, and, like this year, there will be winners and losers in the housing market.
"A recent YouGov poll said 77% of people expect their houses to increase in value next year, and there is a general sense of optimism which may translate into something positive, but I expect the next 12 months will bring more of the same.
"I don't expect house prices to start rising next year. That's not to say won't be sudden peaks in demand for certain types of housing, but there's nothing in the economy to suggest their will be widespread increases in property values."
Kevin Maley, a partner at Strutt & Parker, said: "The outlook for 2013 as a whole remains cloudy and there is much scope for improvement. There is understandably a great deal of uncertainty and a real mixed bag of information in the public domain.
"For example, we have seen the Office for Budget Responsibility predict a rise in property prices for the forthcoming year. However, as I see it, there is likely to be little change owing in part to lenders' caution when handing out mortgages, buyers' worries about their jobs, and sellers' unwillingness to reduce asking prices."
In the past 12 months properties in some areas hold their values better than others, with prices increasing in the north-east of the country fuelled by the wealth created by the region's oil industry.
The most reliable properties in terms of holding their value were detached homes. They continued to remain in demand, while the suburbs around big cities were seen as desirable places to live.
Mark Jamieson, a partner at Corum's office in East Renfrewshire, said: "I think we can remain reasonably optimistic about 2013. There may be general growth in some specialised parts of the market."
Simon Rettie, managing director of Rettie & Co, said: "The volumes of sales in our prime markets of Edinburgh and Glasgow have remained steady. In every market, buyers are continuing to be very selective and not compromising on what they purchase.
"Properties offered for sale have to be accurately priced to attract interest from discerning buyers, who have a wide selection of properties from which to chose.
"An exception to the rule has been the performance of our new Berwick office in England. Having taken over the business in September this year, sales volumes have continued to increase month on month."