I hate cold weather. I have 3 speeds. Slow, slower and stored for winter. All kidding aside, cold weather can be worse for the elderly.
They aren't moving around as much in the cold weather. And if they are trying to keep the thermostat down to save money, they'll get chilled. Just the fact of having older bodies is a reason to pay attention. Their circulation can cause problems. If they have arthritis, the cold will bother them more. Any health issue seems to flair up much worse when you feel cold.
My Mom always said she had a chill when she was sitting doing her crocheting or reading. So keep blankets handy. Shawls and bed jackets are cozy alternatives in the cold weather. A warm cup of tea while soaking feet in a foot bath is a real treat. Same for a warm bath. Filled with something for dry skin.
And there's nothing cozier than having warm feet. Microwavable slippers are a godsend. You can wear them to bed to help with insomnia. (there's a link at the top right on this page for heated slippers. Just click on CosySoles)
If your elderly parents live by themselves, make sure they are taking care of keeping warm. If they live with you, it's easier to gauge how they are feeling. And a nice big warm hug is the best thing for all of us!