The attic check that matters most
Before the first real cold snap, it is worth getting into the attic on a cold day and feeling for drafts around the chimney chase, plumbing penetrations, recessed lighting, and the attic hatch. Warm air leaking through any of those spots is exactly what melts snow unevenly on the roof above and starts the ice dam cycle. If insulation looks thin or uneven, or if soffit vents are visibly blocked by insulation pushed against them, those are worth addressing before winter rather than during it, since attic work in deep cold is harder and less pleasant for everyone involved.
A bathroom fan that vents into the attic rather than through the roof is common enough on older homes that it is worth specifically checking for, since it pumps warm moist air into the one place you are trying to keep cold and dry.
Gutters before the snow flies
A final gutter cleaning in late fall, after the last of the leaves and box elder seed have come down, matters more here than in a climate with a gradual, mild winter. Anything left in the gutter or downspout going into winter freezes solid and stays that way until spring, and a gutter frozen full of debris cannot move meltwater during any midwinter thaw, which contributes directly to ice damming at the eave.
Roof condition before the first snow
A quick check of the roof from the ground, or a proper inspection if it has been a few years, catches lifted or missing shingles, cracked vent boots, and flashing that has started to pull away before winter makes any of those worse. A small gap that lets in a trickle of water in October can be a real leak by the time a heavy snow load sits on top of it for a month.
What to watch for once winter starts
Icicles forming along the eave are an early warning sign worth taking seriously, not a normal part of winter to ignore. They mean heat is escaping enough to melt snow that is then refreezing at the cold edge of the roof, which is the exact mechanism behind an ice dam. Catching that pattern in December, before a dam has fully built and water has started backing up under the shingles, is far cheaper to fix than dealing with a ceiling leak in February.