Fwiw last year ( shortly before X'mas) I noticed my own little Vito's starter seemed to have trouble cranking the engine fast enough to fire up when it was really cold weather. It would take maybe two pre-heated attempts. I found it more irritating than anything, but I had a lot on at the time & was fairly confident in the state of my battery, heater plugs etc, and so I ignored it.
Until
I had finished a late shift, I was tired, it was early morning & sleeting.
Ignition on, pre-heat light out, about half a crank & nothing. Ignition back off, back on, turn to start & nothing, nil, nowt, nada.!!
I'll save you the rest of the sorry details...
Anyway, I determined the starter itself was dead. I fitted a replacement & all was good in the world again (well, maybe not, but my trackday transport was working).
Now to the point of me telling you all that. I immediately noticed that my new starter is substantially faster than my old one was it when was having a good day ( I would say about 30% faster! ) and also it now seems unaffected by temperature.
Hth