The other option is to get one of the few vehicles on the scheme that come as standard with either ‘3 season’ or mud & snow (M&S) tyres as standard equipment.
An exmple being the Jeep Renegade Trailhawk 4wd auto (AP £881) which comes with mud & snow tyres fitted as standard.
https://fcabrochures.co.uk/jeep/renegade/brochure/#page=34
The Jeep Compass Trailhawk 4wd auto (AP £2631) has them fitted as well.
The trouble is you have to search through numerous vehicle brouchure specs to spot them.