Yeah, I'd try some sort of additive like that just to help rule that out as the cause, and b/c it's cheap and easy. Since the tank is full you could just top it off after adding Iso-Heet or whatever w/ a small amount of gas (what will fit) to help it mix quicker.

I'm not sure if the filter would be the cause, but I suppose even w/out water in the gas, a clogged filter could give more of a problem in the cold. If it's as easy to replace as my civic (of same year) you might just want to give it a try if you don't know when it was last replaced.