Nearly two million benefits claimants across Britain were eligible to receive the money in the seven days to March 2, new figures show.
The payments, which are to help with heating bills, are triggered when the nearest weather station records temperatures of 0 degrees and below for seven consecutive days.
Leeds, Harrogate and York postcodes are covered by the station at Linton-on-Ouse, near Wetherby.
Last week's trigger during the Beast from the East was its first of the winter, and around Â£2million has been paid out automatically to the 78,000 eligible recipients in the area.
Around 42 per cent of the cash went to those claiming pension credits.
Those receiving income support and jobseeker's allowance are also part of the scheme.
A week's payment is Â£25 within 14 days of the trigger.
In total, Â£90.7 million is estimated to have been paid out across Great Britain since the 2017/18 scheme began, according to the Department for Work and Pensions.
This is well above the amount for 2016/17 (Â£3.1 million) and 2015/16 (Â£3.9 million), but still below the Â£141.7 million paid in 2012/13.
The government's cold weather payment scheme runs each year from November 1 to March 31.
Payments are triggered by data collected by the Met Office from 94 weather stations around Britain.