Regular physical activity is beneficial for people with all stages of dementia (Alzheimer's society)
Being physically active with dementia helps to slow the decline of brain function and reduce falls, whilst it improves your ability to perform the activities of daily living and do mental tasks (Blondell 2014; Cochrane 2015; Mayo 2011).
Even if you don't have dementia regular physical activity improves your brain function and stops it slowing down as you get older (Cochrane 2008)
Also, physical inactivity is the biggest thing you can change to reduce your chance of developing Alzheimer’s disease (Norton 2014).
People with dementia should be provided with clear written instructions for exercise and be supported whilst doing it; exercising with caregivers can be a great way of achieving this (Venturelli 2011).
Exercising outside is great, but should always be done with company.