I partially disagree with the two other answers (as of the time of this writing).
The Don't.
Let's use a slightly different example sentence to make the nuances clearer:
My classmates don't follow the rules.
This means that the classmates have a general habit of not following the rules. It's form of time-agnostic knowledge; it's possible that you're now attending another school and talking about ex-classmates.
The Won't.
My classmates won't follow the rules.
This suggests that there exists effort directed towards making the classmates follow rules. The phrasing gives an implication that there's an opposing force that's trying to behave your classmates.
Your example.
They don't let you smoke in here.
This is general; the speaker has probably deduced that from a no-smoking sign or similar.
They won't let you smoke in here.
This would imply that the speaker has probably actually tried to smoke once and they didn't let him. You might end up getting the implication that he tried to convince them ('oh, just this one cigarette'), which is the effort we mentioned in our conceptualization.
Note: this is a pretty small and nuanced difference; nobody will get confused if you use them interchangeably, but it does come quite naturally for native speakers.
Lastly: the In.
Simple:
It was getting crazy and hot in here.
This is localized; it was probably getting crazy in a room, hall, or some other enclosed 'cozy' place.
It was getting violent here.
This is more general and can refer to any type of place that is more likely abstractly-bordered-and-contained than having brick-and-mortar walls; think countries and nations, school campuses, streets, etc.
The two have overlapping but not always identical meanings. Both indicate that the speaker is not able to drive to the shop. Depending on the reason for this impossibility, the right auxiliary may be don't or can't or even won't.
- I lack something important for driving, such as a car or a driving license. → can't
- I lack the ability to drive: I don't have the skill, or I'm blind. → can't
- I will not be able to drive that particular time, for example because my spouse needs the car at the same time, or because I plan to be drunk. → can't or won't be able to
- I don't habitually drive. Perhaps I don't own a car, perhaps I don't know how to, perhaps it's a life choice. → don't
- I refuse to drive that particular time, for example because traffic will be exceptionally bad and I hate being stuck in traffic. → won't
Best Answer
Won't implies either a pledge, as in your example (I promise), or a confident prediction, or a refusal:
Can't implies either an impossibility or a directive: