Beta-blockers make cold hands worse. Not good for runners in general as they slow the heart, but sometimes there is no alternative. Beta-blockers are, approximately, the opposite of the Salbutamol inhalers that are so popular in cycling.
Dexshell waterproof socks - NB not Sealskin - worn over the winter, with Injinji liners underneath, prevented my usual chilblains - highly recommended.