Being safe is the number one priority. If you aren't safe, it's silly to attempt anything if it'll harm you. I learned this more than once by making not so good choices. One time it was negative degrees and I took Laura to the bus wearing sweatsuit and fleece poncho. No gloves or ear muffs or heavy jacket. By the time she got on the bus and I was at my gate, my hand was burning, stinging and going numb. I was so terrified that I wouldn't get into my house and no attendant for thirty more minutes. I fumbled with my gate and could open my door. But it took my hand a good 10 minute to return to normal. So, if outside is dangerously cold, don't go unless you're prepared.
I now wear a heavy coat under my poncho. I don't always wear gloves but I will sit on my hands or tuck them in the poncho as we wait. I have an attendant at my house earlier and if it's super cold - she will go instead of me. Plus it's good to know she is there in case I can't get back in the house. If you don't have a poncho, use a blanket on your lap and tuck it under your body. This will contain body heat.
My poncho keeps me pretty warm and repels water. So it is great when it's raining or snowing. These hand warmers are easy to use and they are reusable! They also make toe warmers! Get a microwave heat pad and put it under your jacket. They stay warm for about an hour.
Someone heats up the car for me before going in. Cold makes your muscles tight. I can always tell if I'm cold in a picture if my legs are straight out in front of me. Everything tightens. So being as warm as possible is good.
Wipe off any metal of your wheelchair to protect it from rust.