Could go either way.
His current base clones are no slouch, and he actually has better base stats than her based on his feats of almost matching sasuke's speed, holding his own against deva in taijutsu, saving sakura mid-kunai stab. Boil release would be troublesome for him as the attack covers a good sweeping range and is weak enough that Mei can probably spam it, but strong enough to pop his clones without trouble. That said, he should be able to get in close against her with a bunch of clones considering he only needed 3 to land a hit on kakuzu (who has far better capabilities for dealing with clones than she does).
I think it's safe to say that as a kage, mei should at least have zabuza-level abilities of fighting while in the mist. So naruto will be at a big advantage while in it, however I think he'd be able to blow the mist away if he detonates a COR. If all else fails, base Naruto can summon gamabunta and have him do his giant flame attack.
Mei is a pretty darn good counter to base naruto as she has a lot of spammable techniques that are hard to dodge and would take his base clones out if they are hit. However, due to his feats against Kakuzu, his better base abilities, ability to summon a boss and attack from a distance, and finally the fact that he does have counters to her jutsus I'd say he'd have just as good a chance to win as her.