Phew. Didn't cost as much as we were afraid of. Only ~250€, of which 80€ was tire change and storage fee1.
There was a faulty sensor that reported the cooling system temperature to be a constant –40°C, which in turn fed too much fuel and too little air when the engine was started.
// @matigo @streakmachine
In Finland one needs to use "winter tires" during the winter months and we have studded winter tires which are not allowed to be used during the summer months.