outside of missions?

Weather and time of day is pre-set for the duration of missions in the game, but outside of them yes, there is a day/night cycle.

More specifically: this is not like GTA, as in the story missions are set in the open city, but you cannot move around freely between missions. So during the missions, time of day is set according to the story.

There is Freeride and Freeride Extreme, modes where you can move around freely in the city. You can set either day or night when you start a freeride session, but then you are stuck with that until you start a new one, there is no timed cycle, the sun does not set or rise.

A lot of the story is dependent upon the time of day or night when the events take place.

So they couldn't have it randomly switch from day to night in those sections, or else they would be gimping the atmosphere & immersion factors big-time.

In other words, these designers knew what the heck they were doing!

There is no day and night cycle, in and out of missions.

I'm thinking that "out of missions" is a question based on a false premise, because Mafia doesn't have any "out of mission" parts in its story mode. Does it? Even if you do all your hard tasks in the mission and your goal becomes "Drive back home," that's still part of the mission, and the player is still not "out of mission" at that point.

Plus there are the side missions from Lucas that the game is not sure if the player is going to do or not, so even if the player did somehow complete the main mission and was "out of mission" at that point, then the player would still be "in mission" for Lucas.

Ah, my bad. I was wrong, there isn't a proper day/night cycle like in GTA but a time of day and weather changes throughout different missions.

http://mafiagame.wikia.com/wiki/Free_Ride
What about this?
The wiki claims you can choose between day/night.
What about weather?

It's like Driver 1-3. You select freeride from the menu, pick day or night, and then it puts you in the city under those conditions for the duration of your session. The missions had all kinds of different weather- I can't recall if you can select them for freeride or not.

What about interiors? Are the interiors from Story Mode available in Free Ride?

I think they are. Honestly I recommend you just buy the game. It's an absolute masterpiece.

Of course I will, and very soon. Unfortunately I've read that there aren't interiors in Free Ride, only through mods. But I'll find a way to satisfy my inner roleplayer. :D

I want to add that the environmental design and weather effects are very nice in this game. There is a mission/chapter that takes place on the countryside at night where you see thunder in the distance. It takes a few seconds for the sound to reach the player character, unlike most games and even movies where sound travels at the speed of light.

There is a lot of attention to detail like that in the game which elevates it above it's rougher qualities. It's a passion project and it shows.