If your house is built on a crawl space is there any obstacle to building a covered patio?

How hard is it to add a roof onto the house over a patio on a slab? Or, does the patio have to be a deck?

If it’s a one story house do you need to have the floor of the addition lower than the existing floor in the house? The area does get a little bit of snow, it’s North Carolina, so you need a pitch to the roof.