why wont my heating come on in cold weather?

This fellow is a cowboy trying to make a fast profit. It's almost certainly an ice blockage in the condensate drain pipe, if you have a condensing boiler. Many installations are done without catering for extreme cold like we've recently had. This pipe should be bigger diameter than the 22mm commonly fitted, and/ or lagged with UV-proof insulation. 99% aren't!
Just pour a kettle of boiling water over the pipe length to melt any ice blockage.

Colin
January 2010