You're supposed to use 0w20 in it. It helps with wear on cold startups and gas mileage. Mobil 1, valvoline, pennzoil, castrol, honda and others make versions of it you can find pretty much anywhere.
05-20 is slightly thicker then 0-20. Cold test on 05-20 ultra pennnziol is excellent-I see no reason not to use 05-20 in winter too but with a bit more warm up. A high flow napa platinum oil filter is one of the best you can buy or a mobil one is good too but second best.