The fact that it's a private company does not give it the right to fire people for any reason whatsoever. Employment is a relationship resulting from express and/or implied contractual obligations on both parties. Contract employment binds both parties to the terms of a written agreement, while "employment-at-will" creates obligations most often bounded by objective tests - reasonable expectations and rational relationships to the ability to perform one's duties. You may be able to fire a smoker because their habit interferes with their productivity (and this must be documented). You may fire a smoker because their employment contract contains an agreement not to smoke on the job, or to quit after a given period of time (again documentation would be required). You cannot, however, fire a smoker because they will cost you more to insure them (if so, you shouldn't have hired a person you knew was a smoker). You cannot fire a smoker simply because you don't like the way they smell - any more than you can fire an obese person because you don't like the way they look.
The Government has unfortunately complicated contract and labor law through the imposition of all manner of awful non-objective and punitive (to employers) measures (see: OSHA) so that traditional standards of responsibility and liability no longer hold. As with so much else about modern jurisprudence, common sense went out the window a long time ago, and lawyers helped push it off the ledge.
Smokers are not a protected class anywhere in the US. There is no law anywhere that protects them from being fired for their behavior.
You cannot fire a smoker simply because you don't like the way they smell
Sure you can. There is no law anywhere in this country preventing you from firing someone for having bad body odor.
any more than you can fire an obese person because you don't like the way they look.
Obese people are not protected by the ADA. Only in a very few places are they protected by law (DC being one of them). You are free to hire and fire people based on looks and weight, in most circumstances. As an example, would an overwight model have a cause of action if she was fired for putting on weight? Of course not.