Monitoring the plants for watering needs
should ideally continue into winter as long as the weather is mild and precipitation lacking. The ongoing drought
has worsened again (at least for now) and even if tomorrow's forecast rain is soaking, it won't be enough by itself to catch us up on the deficit. Deciduous plants certainly use and lose water less rapidly in cool weather than they would in summer, but a winter drought can still be damaging, especially to plants still in their first year or two of establishment. Evergreens and semi-evergreens (Sweetbay Magnolia being one of the latter, usually, though complete leaf shedding is also normal for them) will need more regular levels of soil moisture to avoid foliage damage called winterburn, even if such damage doesn't actually manifest until spring.
Feel the soil in the root zone at a depth of about six inches; note that this does not include a mulch layer. If the soil is becoming somewhat dry to the touch at that depth, water well; if damp when checked, the plant probably has enough moisture as-is and you can wait to water. Mulch should be only three inches thick or shallower, though it appears that at least some of the trees may be planted too deeply or over-mulched, since we can't see a root flare at the base of the trunk. To be fair, though, some young trees will not have a very obvious flare until the trunk expands more with maturity. What you want is to have the root flare (the junction of where major roots first branch off the trunk base) sitting just at the soil surface and not covered by soil or mulch. If you do some gentle exploratory excavation to look for a buried flare and find that it's a few inches deep, replant the tree(s) at the proper depth; it will cause them only minimal stress, if any, now while saving the tree from potentially serious root conditions later in life. Information about planting depth and other tips can be found in our Planting a Tree or Shrub
page. You mentioned a Verbena, but we see what looks like a Viburnum shrub in one photo, so presume that is what you meant; if you did install a Verbena, as a perennial that moisture depth can be monitored around four inches instead of six.
We see a couple dead branches (those entirely brown, without any green bark) on the Sweetbay in the first photo, so they can be pruned off now. It appears to be planted very close to the fence, so you may want to consider moving it a few feet further away, if you have the space. The mature size of Sweetbay Magnolia varies with plant genetics; if you have a cultivar, its size will be more consistent, but the wild type can range anywhere from 10 feet (as a shrubby-looking tree) to nearly 25 feet or so. They can have one or several trunks when mature. Although that style of fence probably won't interfere much with root growth, low-lying branches may run into it as the plant fills in; plus, any roots extending into the neighbor's yard will be exposed to whatever they may do to their landscaping (irrigation patterns, any herbicide use for weeds, etc.), so the more you can position on your side of the property, the more control you may have over the tree's care.
Of the trees you mentioned, the River Birch is the most drought-sensitive (at least during the growing season); the Sweetbay appreciates consistent moisture as well, but is more flexible; the Redbud is the most adaptable of the group with regards to drought tolerance, though still could contract at least one fungal disease if drought stress is too severe or consistent.
How much water to apply, whether in duration (sprinkler/hose) or volume (watering can or bucket) is hard to determine, because it depends on your hose water pressure and soil type/drainage. Essentially, you want whatever degree of watering you provide to re-moisten the soil to the same depth you were checking to determine if it was getting dry. You can check it a day or so after watering (or even hours later if the drainage is fast) to see how far down the roots were hydrated and adjust the amount of water applied if needed. Tree watering bags, as an example, can be a convenient way to passively water (they drip water into the root zone for young trees) and hold around 20 gallons at a time, so don't need filling often. Given their vulnerability to freezing, though, they are a more suitable technique to use during the growing season, which is also when their capacity can be an advantage.