What exercises can someone do with a walker?

YouTube has a lot of exercises for someone using a walker.

Yes, even if the person is not a member of Silver Sneakers, they have several videos you can access online at youtube.com. Also, the 2 funny, goofy guys, Bob and Brad (they call themselves the most famous physical therapists on the internet) have good videos on youtube.com and they have a website - bobandbrad.com

Put on some music and practice dancing with the walker! This can be as simple as rhythmic steps and kicking while on the seat, or can involve getting up and down and actual steps while holding on. There are some cute videos of older women dancing with their walkers that will give you ideas. Dancing is really great because it is more fun that simple exercise, less boring, and encourages retention of balance and coordination.

If you search "exercises for older adults using a walker" a lot will come up, particularly YouTube demonstrations.

Perhaps you want her to know (be aware of) safe practices while using her walker? My family members did OT and PT after they started using their walkers. It was primarily while sitting and then walking with the therapist walking along with them. Sometimes with a gait belt. How to sit down and get up or get into the car.
Ask your moms doctor to order her PT evaluation. I did this when aunt went from a cane to walker. I wanted to make sure she was utilizing the walker correctly. They evaluated her and then did exercises and walks.

With the arthritis, mobility problems, vision problems I would probably just encourage walking.
Walking safely though. Not hunched over, not pushing the walker far ahead with arms extended.
There are things she can do at home while sitting.
There are the bicycle pedal things that she can do sitting. Same thing can be placed on a table and can be used with the hands to work the arms.
There are the rubber resistance tubes that she can use with arms/hands to increase strength in the arms.
If you can get her to a Y and swim that would be a great easy way to get some activity in.
I would think a few sessions with a PT and or OT would be a good idea. they can give her exercises as well as assess her strength, balance and coordination as it is.

Walking is great exercise. Walk on level ground or in the house first to build up some strength and experience. After that, increase distance and add a variety of scenes. Before my knee replacements I used walkers extensively because I needed to stop and let the knots in the knees loosen up again. The walker gave me a place to sit wherever I needed one. I used to pick up my Mom and take her to the city rose gardens with paved paths. The two of us would tour the gardens with our walkers, stopping to look at and smell the flowers. We usually spent about an hour in the park, though I really couldn't say how much of that was walking and how much was sitting. We had a good time and we probably covered about a mile of walking while having fun in the gardens. Walking the mall can also be an interesting outing that makes the walking (and exercise) seem like a side issue, with the main event seeing what the stores have. For any exercise goal, it is easier if one has fun in the doing, not just trying to attain an abstract goal.

There are a lot of videos of "chair exercises" online.

Ask the doctor to prescribe physical and occupational therapy. Often these services can be performed in the home and paid for by Medicare.

(I am a rep.for Rebound Air). It is amazing to me the strength we can get by Rebound exercise. A person can sit on the rebounder and bounce or someone can stand behind the person sitting and it is 3x the benefit of normal exercise.
If you have questions, contact me.