My brother in law used to have cold flat. He had a gas cabinet heater on one side of the room for the cold, and a dehumidifier on the other for the damp.
I use a door heater curtian heater and wall mounted frost free heater and shead loads of insulation. So far no ill effetcs on the tools or wood. Oh, and I sealed the walls with block wall paint and used an sealing floor paint on the floor and I have sealed the up and over with insulation, moisture membrain and 18mm MDF.
Went into the shed this afternoon and whilst it isn't warm - no vapour to be seen when breathing out, so can't be that cold, but the shed is insulated to the eyeballs. Suspect just moving about or doing stuff would keep a person warm enough.