Or OP may be referring to overnight connection as booked, even without delay. The only time I have heard of this is some specific airlines in PAID first class on long haul international travel. Even then airline specific.

No, the answer is exactly the opposite of what OP seemed to think. Most overnight layovers do not receive any hotel room, that is up to you.

Agree with above that with delays, sometimes this is done for mechanical delays but generally not for weather. Sometimes the high level elite passengers will get special consideration, but not the masses.