Prices in winter do rise for heating oil, natural/propane gas based on how cold it gets and for how long.
In AZ and CA gasoline prices will generally go down because the winter blend additives cost less than the summer blend.
Also much less traveling in winter.
This happens in Nov-Feb more times than it doesn't. Here is the link to see it.
Gas prices in AZ depend on where the gas is piped from. For Phx area gas comes from California (it can be .30-70 cents per gallon more vs TX.)
Gas for Tucson area is piped in from Texas (it costs less)
Also areas outside of Tucson and Phx don't require the winter summer blend fuel required by the EPA Air Quality people ,
that saves $.20-35 cents per gallon,