A total of 39,905 mortgages were approved in January, 6.2% fewer than in December, and 17.4% fewer than in January 2010.
The remortgage market also suffered its first monthly fall in December since June as volumes fell 5.2% month on month in January.
Just 29,000 remortgages were approved during the month, slightly below the average of the previous six months, but still well ahead of the extremely low levels a year ago, up 17.9%.
Purchase volumes fell by a similar amount across all price bands up to £750,000.
Richard Sexton, business development director of e.surv, says the snow has meant far fewer people able to get out house-hunting in December.
He says: “As a result, fewer applications for mortgages were made and that has led to a sharp dip in approvals. But this has merely exacerbated the underlying weakening trend in the housing market. As the economy has slowed, so too has the appetite to move home.
“House prices are flat or falling slightly so prospective buyers feel less inclined to rush ahead with buying a new home. A similar fall across all price brackets supports this view.
“At the same time, lenders pulled back from the market in December and January after a very strong November when there had been a bit of a competitive flurry to meet annual lending targets.”