Yes you should opt for fully synthetic and 5w30 is great in winters (and summers too if you dont drive for hours in high noon with AC) If your running is a lot in rush hour traffic at peak temperatures then w40 should be considered.
smaller number (5) means the viscosity when engine is cold (thin)
larger number (30/40) means the viscosity when engine is hot (thicker)
My civic 05 is running on 5w30 since day one (islamabad/pindi) but usage is not very high in extreme temperatures