LONDON CORN EXCHANGE, Wednesday, Jan. 3. -- The weather has become intensely cold, and we had a sharp frost last night.  The English Wheat was mostly cleared off on Monday, and but little further supply has since come to hand.  The demand for foreign has improved, but so many holders having raised their pretensions has checked business.  There was very little done in barley, chiefly in consequence of so few maltsters and distillers being at market.  We have no additional arrivals of Irish oats, and only two or three coasters, since our last market day.  Considerable progress having been made in sales of late supplies, and the market being comparatively bare, needy buyers had to pay rather more money; but the sales were mostly in retail.  There is more firmness in the trade, which wears generally an upward tendency.