Speculation surrounds the future of the payments which are being examined as part of a radical shake-up of the welfare system designed to save billions of pounds.
Labour called on the coalition to "come clean" about the plans and public service union Unison's general secretary Dave Prentis warned cutting the winter fuel allowance could cost lives.
Deputy Prime Minister Nick Clegg said savings had to be found in the welfare bill, while stressing that no final decisions had been taken ahead of October's Comprehensive Spending Review.
The coalition agreement between Mr Clegg's Liberal Democrats and the Prime Minister's Tory party pledges to "protect key benefits for older people such as the winter fuel payment", but does not rule out reform.
But Labour pointed out that Mr Cameron had explicitly ruled out scrapping winter fuel payments during the general election campaign.
Shadow foreign secretary and party leadership contender David Miliband said: "Up and down Britain, pensioners rely on this benefit to get by. The payments Labour introduced mean many pensioners can heat their homes without worrying and fretting over the energy bill to come.
"The Prime Minister's dishonesty is unacceptable."
Mr Prentis said: "We cannot begin to call ourselves a civilised society if the Con-Dem Government allows elderly people to sit in the cold or freeze to death in their homes.
"They must think again if they are seriously considering cutting these payments, particularly to the very old, because they save lives."
The National Pensioners Convention also warned against changing the winter fuel allowance system.
Dot Gibson, NPC general secretary said: "The winter death rate amongst older people is a national scandal and getting worse.
"Last winter over 36,700 pensioners died of cold-related illnesses - a staggering 13 pensioners every hour.
"Yet the Government is now considering taking the winter fuel allowance away from millions of households which will only make matters worse."
According to reports, the Government is considering raising the age at which people become eligible for the annual winter fuel handout from 60 to at least 66.
The payment - worth £250, or £400 for the over-80s last winter - could also be cut by £50 for new recipients and £100 for the oldest.
Child benefit could also be reduced in order to fund root-and-branch welfare reforms proposed by Work and Pensions Secretary Iain Duncan Smith.
Interviewed on BBC Radio 4's Today programme, Mr Clegg - covering for Mr Cameron while he is on holiday - said: "It's the middle of August. This is not going to be announced until October. And final decisions will only be taken much nearer the time.
"I think it actually increases anxieties in having this constant running commentary on decisions that haven't been taken or might not be taken at all."
He added: "We are engaged as a Government in a collective effort to get this right to both make savings to the welfare bill and to create a simpler, fairer welfare system that, above all, gets people into work."
At a question and answer session later, Mr Clegg declined to give his "personal opinion" on whether the allowance should be reformed.
He said: "I have made it quite clear that the comprehensive spending review will be concluded in October.
"We have made it very clear - I have made it clear, George Osborne has made it clear, the Prime Minister has made it clear - that what we want to do in every area of the comprehensive spending review is not duck the difficult decisions but to try and implement them as fairly and equitably as possible."
Winter fuel payments, introduced in the winter of 1997, cost about £2.7 billion a year.
Although Mr Cameron pledged to keep the winter fuel allowance during the general election leaders' debates, the Liberal Democrats campaigned on a platform of reforming the payment by raising the age threshold to 65 and giving severely disabled people more.
The qualifying age for winter fuel payments is already rising in line with the increase in women's state pension age - set to equalise with men's at 65 by 2020.
Ministers have proposed speeding up plans to raise the state pension age for men to 66, possibly by as early as 2016.
The Department for Work and Pensions and the Treasury are believed to be locked in a battle over funding the short-term costs of Mr Duncan Smith's plans for welfare reform at a time when Government departments are being ordered to make huge spending cuts.
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