If I purchase a MacBook Air on the 1st of January will it be a early 2016 model or still come up as a late 2015 model?

It will be the current model which is the Early 2015 model. There has not yet been an official announcement of when the next model will be released.

So, all of the Macbook Airs that I see on "Refurbished For Sale" on Apple website( dated March/spring 2015), are no different than the ones for sale now in the stores?

That is correct, except that they are refurbished. The current model is the Early 2015 model. See the attached link for a list of all models: How to identify your MacBook Air - Apple Support

Thanks-it seems that many have noted that refurbished has never been an issue for them. The cost savings isn't great but I suppose it can be used towards Apple Care.