Nice thread title.
I imagine it would look a lot like Mexico and the Carib, only with colder winters.
Thing is, if that is so, what would draw Spain to colonise New England? The Caribbean islands are plantations. Mexico provides a constant flow of mineral wealth. These are almost purely exploitative in purpose, with settlement as is required to function effectively. Why would they do the same to, for instance, Maine, which can offer little of obvious worth beyond timber?
I think the most likely course of Spanish involvement in the region would be similar to that of the French in OTL: a few coastal trade depots, limited settlement, and an economy based around the fur trade - interaction with most natives and the interior is mostly the preserve of trappers and missionaries. Maybe after some time has passed we eventually see settler colonies more in the manner of the English.