@assaultpotato Thanks for your reply!
I haven't cycled with snow that much because I got a front wheel engine and it's got too much power to control in those conditions. But I have definitely dealt with gunk! It is just so strange that it is only *that* connector. It may be a "feck you in particular" kind of situation.
After fitting the rubber seal, the battery works again, but seeing the state of that connector, I'm worried the shaking will cause more damage.