You should definitely warn Steve (discretely).
... and I'm surprised other answers have not taken this position (more on that point below).
You are not your company. You do not control it, it is not acting in your best interests. It is an instrument for its owners to make a profit (and a social instrument only indirectly). You're a salaried employee, as is your co-worker Steve. You have much more in common with your co-workers in terms of collective, and probably even personal, interest than you do with company management.
I can't help to feel that I should warn Steve somehow, as it seems unethical to fire him without any previous notice (thus affecting him greatly)
Steve is subjected to the underhanded treatment of termination without notice, and the even more underhanded treatment of hiding the already-decided impending termination from him. Did you know that in most countries with any past of union movements, workers have pressed employers and government and have made this practice illegal? In quite a few places where organization is stronger, termination requires a justified cause adjudicated by a bipartisan committee of employers and employee representations (unless it's for something like stealing from work etc.)
Even though I feel like warning him, this seems to be a bad decision.
No, it is a good decision (assuming you do it carefully).
If you were to only consider your own short-term self-interest, then - why tell Steve? Who cares, right? He's getting the boot, not you, and you're afraid if you misbehave you might be punished or suffer the same fate as him.
But that's the wrong way to think about it. All of you at that company must be able to rely on each other to be supportive and helpful - as the company is inherently not. Steve is depending on you to help him out, like you may depend on others to help you out, in some other situation in which management self-interest may harm you. You should consider his interest and well-being - as well as that of his family and community.
Now, I didn't say you should try to thwart his termination; but don't betray your coworker. Rather, stick up for him. Find an opportunity to suggest that you guys talk after work, not at the workplace, and explain the situation. You will also get a lot more information from him, which currently you're not getting. This will also help you decide what you want to tell your manager - that you'll oblige, that you can't, that there's this or that kind of problem etc.
I'd even say you should talk to Steve before discussing this again with your manager. Coordinate with your fellow workers first, and with management later.
I believe this is the result of the combination of two factors. The first being that most users / answer authors on this site, and this page particularly, are from the USA; and the second is the ever-continuing weakening of working-class organization and education in the US. Pro-employer mores and social conceptions face you wherever you turn - in the lawbooks, from the politicians, the businesspeople of course, the courts, the collaborationist corporatized unions, even the education system.