I have heard that you should use a multigrade oil with the narrowest band of viscosity that is appropriate. Is this so?
Yes, in the winter base your decision on the lowest temperatures that you will encounter and in the summer the highest temperature that you expect. In general the greater the oils viscosity range the more the oil is prone to viscosity and thermal breakdown, do to high polymer content. A 10w-40 and a 15w-30 require a lot of polymers which is what they add to an oil which allows it to get thicker when it gets hotter, but it does not lubricate. Group III and group IV oils use polymers in order to achieve that range of viscosity. Polymers also burn with forms ring sticking deposits and other problems. The more polymers there are the less oil there is in the container to lubricate your engine. Overall it’s best to avoid polymers, and do that by using group V oils.