The system you are describing is not a wood fire. In your description, the unit where the wood burns could be called a wood-burning stove (or wood-fired stove), and the whole system of radiators could be called a wood-fired central heating system. Note that 'fire' is a verb here. If you say 'We have a wood fire', you're describing something else. We would understand that to be a fire lit in a single fireplace that would be the focal point of a room. Something like this: https://www.housebeautiful.com/lifestyle/g24799592/how-to-light-fireplace-indoor-outdoor/

https://www.totalswindon.com/images/content/Stock%20Images/SEASONAL/Winter/fire_ss142464652.jpg My first immediate thought would be an open wood fire, which is associated with ‘warm’ and ‘cosy’ winter nights, as shown in this picture. The person “always” has a fire in the house in the winter, so I would assume it is an open fire for particularly cold winter nights. Also, the writer mentions ‘village house’, which suggests it could be an old, small or more traditional house (and therefore more likely to have an open wood fire).