I don't have any experience in your zone, just my much colder zone, but I cease watering when the ground freezes even a little bit. At that point water won't penetrate so it's pointless.

A common cause of winter injury, believe it or not, is drought stress. The winds can dry the above ground portion of the plant and without accessible water the plant can't compensate.

Does the ground freeze in your part of AZ? I know some parts get snow and others usually don't so I am not sure what you experience. If the ground doesn't freeze then I suggest watering all year, just back way off on the frequency as temps drop as the tree won't be using it as quickly.

Plants require water in winter just as they do during the growing season. If you don't receive regular and sufficient rainfall, you will need to continue to water. Plants in subtropical regions also tend to experience little if any dormancy (or it is restricted to summer) - if you are truly a zone 10 you would be considered in this region. However, zone 10's are typically frost-free - if you have temperatures dipping into the 20's, you may be in quite a bit lower zone.

At any rate, barring enough natural rainfall, continue to water through winter at a rate of 5 gallons per inch caliper per week for evergreens or non-dormant trees, less for dormants plants.

Please read the attached great link on trees. Click on 'Establishment' and once you get into that chapter, click on 'Irrigation' to find the answers to your questions. Most people either greatly under OR over water their new trees. Both are equally harmful to the establishment period.

Here is a link that might be useful: Tree establishment

I suspect that you are referring to the Sunset system of assigning climate zones, right? If so, that that might put you (roughly) in a USDA system of around 7.

That's just a stab in the dark, though.

If you read the first installment in the 'Establishment' chapter, I believe that Ed talks a little bit about the difficulties of tree establishement in a desert-type climate.