To firm up the whole tree (and this is where the paper-covered wire comes in handy, although plain floral wire will also benefit from this next step), I cover most of the tree with full-strength Elmer's white glue (Glue All). I generally apply the glue on all branches where two or more wires are twisted together. I use a fairly stiff small brush to really get into the nooks and crannies.
Obviously, the tree's branches clearly show the twisted-wire shapes throughout. The next step is to hide these, and to add additional forming and shaping to the branches. I use Liquitex' Flexible Modeling Paste (available at most hobby and arts-and-crafts stores). It is easy to work with, doesn't have much of an odor, and indeed leaves the tree somewhat flexible. I have also used Woodland Scenics' Flex Paste. It works the same way, although it is a bit thinner than the Liquitex product. The preserved flexibility helps when you accidentally bump the tree while reaching into the layout. The tree will give and move back, without breaking. The modeling paste is somewhat expensive, but a jar like this will last a long time.
Much like the white glue layer, the paste is applied with a stiff brush. The entire tree needs to be covered with it. This is probably the most time-consuming step, but it is an important one, because this determines the final shape and look of the tree. I apply two or three coats of the modeling paste; whatever it takes to get rid of the twisted-wire look of the branches. I let each paste layer cure overnight. I like to apply liberal amounts on the main trunk, because that gives the tree its massive look. One of the things I like about making these kinds of trees is that you can be sloppy. You don't want to be too exact and precise. You want randomness. This photo shows the tree with one layer applied, so you can still see some twisted wire here and there.
While building another set of trees, I wanted to experiment with applying some sisal/twine/rope branches. I cut pieces of the twine around 1/2" to 3/4" in length. Next, I used white glue and a brush to apply the glue judiciously to the ends of the main branches. Next, I sprinkled the twine pieces onto the tree. A couple of quick spins of the tree (using the toothpick in the bottom) will make the twine spread out. By applying the glue to specific areas you can control where these thinner branches will appear. The photo shows the result. The white glue will set fairly quickly. After an hour or two they are on there fairly permanently. This experiment was successful, and it is the latest method I use to model thin branches.
After the modeling paste has cured, the next step is to paint the tree. You can use any acrylic paint, spray-paint them, or even airbrush them. For trees like the one in the previous photo you pretty much have to spray-paint or airbrush them. If you don't use the twine branches, then hand-painting of the main trunk and branches is entirely doable, as I have done to the tree in the photo below this one. For that one I used Liquitex "Burnt Umber" as the main color, with highlights of Delta's Ceramcoat "Dark Forest Green". I didn't mix the paints. I simply dabbed the brush in the burnt umber most of the time, and then occasionally also dipped it in the green. You wind up with streaks or spots of the green color, which will make it look like moss is growing on the branches. Also, I tend to go more heavy on the green when I reach the ends of the branches to blend them better with the tree foliage later on. I use a long-handled brush to be able to easily get into the inside of the tree (see bottom of the photo). Putting the tree in some sort of stand makes painting it go much easier. I use my bench vise for this. By the way, I superglue a toothpick into the bottom of the tree. This helps with holding it, and later with planting it in the layout.
And this is what the tree looks like after the painting session. I usually have to come back after the paint has dried and touch-up areas that I missed. When the paint is wet, the light reflects off of it and you can't tell the difference between wet paint and the white of the model paste underneath. These paints dry mostly flat, so when they are dry, it is easier to spot missed areas.
The "spiky" version of the tree has to be spray-painted, as painting the individual sisal branches would be too time-consuming.
The next step is to dry-brush white and/or gray to the main trunk and large branches. This gives the tree a more three-dimensional look and simulates sunlight reflecting off of its surface.