third generation cavaliers have an electric solonoid at the shifter that is a 'lockout' device, wired to the brake light switch, wich is why the label on your cluster reads 'apply brake to shift from park' --its a direction; not a suggestion. if the solonoid is dirty or dying, the cold will keep it from working well [kinda like the way old power windows don't work right in winter]
long story short, axe it, or diagnose the electrical issue. it is there just as a safety precation for accidentaly knocking the vehicle into gear.