Why not step in for an elderly person. Don't ask, just do it. There is no reason this should not be done. It is for safety and it is an act of kindness. Shoveling is a quiet job, so if it is done at the right time if someone does not want to be heard, it can be done.
Also, if you think the person would like to thank you there are many ways for this to be done.
1. After the job has been done let the person know you wanted to shovel their walk as you just did yours, and stress theirs is no charge, but is there anything else they would like.
2. If they are not home leave a note telling them who did the act of kindness.
3. A different note this time with both name and telephone number in case they need anything.
Winter weather can be hard on our mature adults as they can get cabin fever as they must stay indoors due to the harsh cold temperatures. Just knowing they have a friend that cares about them outside will make them feel better about the winter weather.