Firstly to understand how art can strengthen your cognitive skills we need to briefly understand what they are and why they are important. Then we look at a list of some specific cognitive skills. Then we can understand how learning how to draw can have a direct or indirect impact on strengthening particular cognitive skills.
The term cognition (From the Latin cognoscere, "to know", "to conceptualize" or "to recognize") refers to your ability to process information, apply knowledge, and change preferences.
Cognitive processes, can be either conscious or unconscious. Cognitive abilities are the brain-based skills and thinking processes that you use to carry out any task — from the simplest to the most complex. Every task you do can be broken down into the different cognitive skills that are needed to complete that task successfully.
Just like any skill, if you do not use your your cognitive abilities they will get weaker over time. Fortunately, these skills can also be improved at any age with regular practice.
Below are some of the basic cognitive skills that are used to complete some of the more complex tasks at work or home. As you scan through the list you can readily recognize that learning how to draw or paint may have a direct impact in exercising or developing that particular cognitive ability. For others the reason may not be as evident.
Alternating Attention: the ability to shift the focus of attention quickly.
Auditory Preprocessing Speed: the time it takes to perceive relevant auditory stimuli, encode, and interpret it and then make an appropriate response.
Central Processing Speed: the time it takes to encode, categorized, and understand the meaning of any sensory stimuli.
Conceptual Reasoning: includes concept formation, abstraction, deductive logic, and/or inductive logic.
Divided Attention: the capability to recognize and respond to multiple stimuli at the same time.
Fine Motor Control: the ability to accurately control fine motor movements.
Fine Motor Speed: the time it takes to perform a simple motor response.
Focused (or Selective) Attention: the ability to screen out distracting stimuli.
Response Inhibition: the ability to avoid automatically reacting to incorrect stimuli.
Sustained Attention: the ability to maintain vigilance.
Visualization Classification: the ability to discriminated between visual objects based on a concept or rule.
Visualization Sequencing: the ability to discern the sequential order of visual objects based on a concept or rule.
Visual Perception: the ability to perceive fixed visual objects.
Visual Preprocessing Speed: the time it takes to perceive visual stimuli.
Visual Scanning: the ability to find a random visual cue.
Visual Tracking: the ability to follow a continuous visual cue.
Working Memory: the ability to hold task-relevant information while preprocessing it.
For the visual and visuospatial abilities there is a clear benefit in the practice of drawing and painting. Similarly for the fine motor skills.
For the attention based abilities there is an easily recognized relevance between art and the "Focused Attention" ability. Also it is likely that specific drawing exercises such as sketching a model in rapidly moving poses may assist in exercising the "Alternating Attention" ability.
Central Processing Speed is an interesting area for discussion. There is evidence that the visual "right brain" has a significantly faster processing speed than the mathematical "left brain". This is highlighted when you consider that a computer can perform calculations at a rate far superior than a person - but even the worlds fastest computers struggle at visual tasks such as facial recognition.
It is possible that "Conceptual Reasoning" can benefit from art in a number of ways. The process of drawing that takes a set of visual elements (lines, shapes, tones) and organizes them into a higher level framework. Abstract art takes a real item and creates a new but related image - exercising concept formation.
Also the ability to perceive and correct differences between a subject and a drawn image is relevant to the "Response Inhibition" cognitive ability.
Finally for some of the auditory skills the relevance may not exist at all. (To exercise those you might like to take up a musical instrument as well)
So in summary the activities involved in drawing and painting would also provide a way to exercise many of the cognitive abilities. If you want to maintain or improve your ability to to perform higher level tasks then art can provide the necessary "drills" while being a highly pleasurable activity in its own right.