A brake cable and derailleur cable can be life savers. Same for a straddle cable for cantilever brakes. A few spare bolts, such as water bottle cage bolts, can come in handy. Same for a folding tire. That ought to suffice unless you need to get into the expeditionary mode and that's another story entirely.
Extra clothing is mandatory.
At a minimum, you ought to have a rain suit - a waterproof rain suit, not a water resistant rain suit. Also a jersey made out of either wool or a synthetic that insulates even when wet. Tights in a similar material can be appreciated too. Same with gloves and a warm hat. Whether more than that is needed can be determined by paying attention to weather forecasts.