the question is whether this area should be covered or not with the solder mask?
- I normally leave it covered by mask. However I need to say, usually I design different kind of boars (e.g. often I have multiple GND planes and heatsink available)
I wanted to know the solder mask has a role in the heat dissipation in the air.
- I have never experiment with this, but I would say, solder mask will influence heat dissipation
In the case of solution B, could I have trouble leaving that big exposed PAD, such as oxidation or something like that?
- if you do gold finish, I believe it should not oxidate
If the heatsink area is GND, I would probably not worry about making it big and unmasked. If it was not GND - then I would be more careful - making it big could cause problems with EMC/EMI and in that case it may be better to consider placing heatsink on the plastic package of the chip.
We often use thermal adhesive tape + simple and cheap heatsink (it is cheap and quick solution). Looks like this: