1996 BMW 318is with freak headlights

My 1996 BMW 318is has freak headlights. When the weather is cold, the headlights sometimes do not turn on when needed, and even stranger, when I get to my destination, they won’t turn OFF. Running lights, fog lights, and high beams all seem fine and function as desired in all weather conditions. Freaky huh? Winter is coming, I don’t want to be stranded at night. Ideas???

In the dark in Dallas,