Do you need to water established trees beyond rain & snow melt?
Larimer County Colorado
Yes, if we have warm days without snow cover and you have the ability to water, it's always wise to water your trees and shrubs. Keeping the soil moist all year is a great defense in preventing additional stress to these plants.
The snows we've had haven't had a lot of moisture in them. They have been "dry" snows. Try to water on days above 40 degrees and keep an eye on runoff. Only apply water when the ground is actively absorbing the moisture. If it starts to run, then move your sprinklers.
Here's the fact sheet on Fall and Winter Watering: https://extension.colostate.edu/topic-areas/yard-garden/fall-and-winter-watering-7-211/