no money is happiness.
just kidding. obviously you can. but the problem is that other people get jealous of people who actually live without money. Well the problem is the problem. I think it depends on notions of civility. Whether a Stoic Philosopher can exist in a non-civilized environment.
The sound of the question is wrong. No you can't "without much money". It's either none or all.
Back in Greece though, where civilization once existed:
Stoic Philosophy contends that nature and morality are happiness. If you sacrifice your morality, your innocence, or your nature or both, you cannot achieve happiness.
No you can't lead a happy but poor life. People who are genuinely fooled by the world will become unhappy through its pursuit.
The happy bum though, yea. Well not today where bums are people who can't afford their drugs.
But Stoic Philosophy is reality, the reality of happiness is morality. The reality of happiness is not money, but many will agree that excessive money is the second best thing to Stoic Philosophy, which is not hardship either.
But no there's no in the middle where desire for the world will ever be happiness. ANYBODY can be a Stoic Philosopher, not anybody can be Alexander the Great. But there is no middle happiness. They are always extremely desperate for happiness.