St. Hilary's Day - weather superstitions - from PROJECT BRITAIN web site

St Hilary's feast day on 13th January has gained the reputation of being the coldest day of the year due to past cold events starting on or around this date.
One of the most severe winters in history began around 13 January in 1205, when the Thames River in London froze over and ale and wine turned to solid ice and were sold by weight.

"So began a frost which continued till the two and twentieth day of March, so that the ground could not be tilled; whereof it came to pass that, in summer following a quarter of wheat was sold for a mark of silver in many places of England, which for the more part in the days of King Henry the Second was sold for twelve pence; a quarter of beans or peas for half a mark; a quarter of oats for thirty pence, that were wont to be sold for fourpence. Also the money was so sore clipped that there was no remedy but to have it renewed."
—Stowe's Chronicle

In 1086, a great frost also started spreading over the country on St Hilary's Day.

http://www.projectbritain.com/calendar/january/hilary.html