Draughts - what to look for
Inspect around doors, window frames, bare floorboards, cat doors and ceiling hatches. If there's a hole larger than around 2mm it would pay to get this fixed. There are a range of draught excluders available from DIY stores.
A note about open fires: these might seem like a cozy addition to a home but in reality they are very inefficient heaters and let a lot of warm air escape up the chimney - it's like having a window open all the time. It's better to close this off either permanently (capping the chimney) or temporarily, with a balloon (available from some DIY stores) or just a bag full of old rags. Remember to make this visible to any future occupant, in case they try to use the fireplace!