How does your son do on the Marshmallow Test? If he has poor deferred gratification skill, then he may lack the patience to acquire talent. Even so, never fear! This skill, like all others, can be practiced and improved! The "greedy marshmallow" strategy is actually quite rational. It doesn't make sense to wait unless the future reward is bigger than the currently offered reward. What does that have to do with painting miniatures? Well, it means that your son shouldn't keep trying his hand at it unless he believes that he will get better. So, show him that he can improve.
Siskel & Ebert
In order to improve, your son first needs to know what "good" looks like. He needs to become a critic. Apparently, he has some sense of what "good" is already: "what dad did." That's a start, but you want him to get precise. When he looks at your model and says he wants to paint something like that, ask him what he likes about it: is it the color? The detail? The texture/finish? Then ask him to critique his own work. If you agree with his analysis, then say so! He needs the feedback to tune his inner critic. If you disagree, you can pose your disagreement as a question: "I screwed up because my guy has a red face and yours has a green face." "Well, your guy does have a red face, but mine has red eyes. So is red really the problem?" "No, I guess not. I tried to paint red eyes on my guy, but I couldn't, so I just made the whole face red." "Ok, so we just need to practice painting eyes!"
You not only want to teach your son how to improve, you want to teach him how to figure out on his own what needs improvement. This enables self-directed learning once he reaches a certain level of proficiency. And by using a Socratic method, you get him to say the critical point himself, which reinforces the authority of it. That is, we remember facts better when we believe we have arrived at them ourselves rather than having them spoon-fed to us by someone else. Socratic questioning is an art, but done well, it teaches the student not only the answer, but also the path to the answer.
Practice Makes Perfect
Let's suppose that one of the problems is fine motor control: "I tried to paint a blue wrist band, but I couldn't." If you want him to wait 20m for a marshmallow, you have to offer 5 marshmallows. In this case, you need to show him that some practice will actually make him better in the future. You can do a simple demonstration yourself. Pick some simple task that you know you are not good at, like, drawing some figure. If you're a good artist, try drawing with your non-dominant hand. "Look, dad drew a box with his left hand. Tell me what you think." "Well, the left side is crooked, and the top is wiggly." "Yup, I agree. Let me try again." "Now how does it look?" "Well, it's better, but the left side still looks wrong." "What looks wrong about it?" "I think it's shorter than the right side." "Yeah, let's rotate it and see if we still think so. Yup. Now the right side looks shorter. I think you were spot-on!" 3-4 tries later..."Wow, that looks really good! I can't believe you drew that with your left hand!"
"Do you think I have magical powers?" "Haha!! No!" "You're right. The only 'magic' I used was practice! Now, let's draw some eyes for you to paint." Start out with big, easy eyes, let him make an attempt, self-critique, and then evaluate. Then make them smaller and more difficult. Then smaller again. Show him through easy increments that he can improve with even a modest number of attempts. He can now see that plate of marshmallows in his future!
Cognitive psychologists have discovered that we learn best when we are challenged right at the horizon of our ability. If a challenge is too tough, we fail without learning much. If it is too easy, we succeed without learning much. That balance between failure and success is where we learn the most in each attempt. You are doing well if you present your son with challenges that have about a 50% chance of "failure", as defined by him.
Initially, his inner critic will be crude, and only notice the biggest features. That's ok. Encourage all insight he displays, and gently correct evaluations that will lead him astray. As he gains more confidence, demand more detailed evaluation. Play devil's advocate, and argue that something looks better even if you don't personally agree, and make him explain why you are wrong. So you need to train both his skill and the evaluation of his skill in parallel, as they will tend to reinforce each other.
In the end, you want to demonstrate by your actions that being bad at a new skill is not something to be embarrassed, ashamed, or frustrated over. Everyone starts that way at every new skill. Ask your son to try something new with you that you have never done before, so he can see you be awkward and "fail" at it (bowling, paper airplanes, model rockets, juggling, frisbee golf, etc.). Showing that learning is fun is your goal. Eventually, he will learn to relish the challenge of learning something new, even if he starts out as an utter failure.
Maybe you could pick some miniatures in a style/game you have never played before. Your first attempts will likely be better than his, but demonstrate your own inner critic in action, and narrate how you will try to improve, so he also sees the introspective portion of learning in action. When you make a mistake, call it out, explain that you didn't mean to do that, or shouldn't have done that looking back, shrug it off, and try again.
Your ultimate goal should be to help your son acquire expert-level proficiency at something. Almost anything. That single achievement unlocks a world of possibility in his mind that will help him achieve almost any other goal he sets. But getting there involves crossing a daunting mountain of frustration. Even though learning can be quick at first, it soon becomes a slog. At some point, only grit and determination will get you through the boring repetition of acquiring high-level skill. And that is where he will need the most encouragement. I have high hopes for him, though. It looks like his dad has already acquired expert-level skill, so he has a good role model. ;)