When to stop watering (deciduous shade trees)

I'm in a high altitude desert environment, USDA zone 7a. I've planted some Lacebark Elm trees (https://www.arborday.org/trees/treeguide/TreeDetail.cfm?ItemID=838) that I got from my state nursery, and they've been doing really well. I think they were in ~3 gallon pots. I planted them and have them hooked up to a drip system, and they honestly look like they're thriving.

Winter will be coming soon, and with it will be our cold temperatures. I'm guessing these trees will drop their leaves and go dormant until the spring, so do I need to water them at all? Should I just stop watering once it's getting too cold for the on-surface drip system?

I water trees for the first year. If it is a dry winter I would water the tree in late winter a few gallons per tree . Tree roots can dry out in the winter and can cause issues the following year. This is a it depends on the weather when and how long to water the trees.