I always fit a full set of “All Season” tyres at my own expense regardless of it being my own car or from Motability, if you do then all the upkeep is your responsibility even punctures but you can do it.
At the moment I have just had a full set of Maxxis Premitra All Season AP3’s, should have cost around £580 fitted but my local fitting centre is an authorised stockist and did me a cracking deal, £400 all in.
The difference between these and the crappy eco summer tyres is night and day, been out in all weathers over the years and not been stuck once in the 10+ years I’ve been running them on several cars, I can’t afford to get stranded in bad weather same as most disabled folk I’d imagine.