I'm pretty sure you can only claim a 100km or more section as part of a longer DIY, but you can do the hilly 60km section and the 110km for fun!
You can, of course.
It's one of these things though... sounds great in May, but then I run out of steam in September. I think winter is a good opportunity to rest and be fresh the following spring, rather than risk a collar bone or worse for the sake of a badge.
I never found the saying "winter miles summer smiles" to have any truth in it... if anything it is the exact opposite... those who cycle long distance in winter seem to get to April completely worn out.
If you look at the professional circus, before it went global and found a summer somewhere on the planet at any point in time, the racing season began in March and finished in October, the rest was cyclocross, which is generally a high intensity, short duration effort and free of ice