As long as you have not explored an area, which means that you have not gotten closer than roughly 500 meters by foot or ship, then the first time that you use your old map it will update those unexplored areas.

It means that it will take a little while longer to start that first time, but that is normal. Thus, you'll get the glory that are the caves, pits and so on as long as the areas are big enough.

So, go and... I was going to say that those mobs won't kill themselves, but then I remembered the loxes, fulings and undead among others. Thus, go and party on, don't let the mobs have all the fun!

Edit: As long as you are exploring the mountain for the first time, there's a chance for one or more caves. It's somewhat random, as long as the mountain is big enough then there's a chance.