Is planting trees really the solution to climate change?

I often read articles suggesting that planting more trees is the miraculous solution to climate change (such as this one and this one, for a random selection). It's a comforting and pleasant thought. And then I read other articles pointing out that, while this might help to same small extent, just planting trees, even on a massive scale, is not going to be anything like enough to address the problem, and whether such a plan is anything like practical is far from certain. So, I decided I needed to understand the carbon process, as it relates to trees and other vegetation, a bit better.

I found an excellent article explaining the real relationship between trees and carbon dioxide, as well as the various models of understanding that regular folks have about them (and how close to reality they actually are). The article points to six main conceptions that people have about how trees affect our climate, some of which are more accurate than others:

1. Trees filter carbon dioxide from the air - this is perhaps the least useful or accurate one: it suggests that trees take the "bad" things out of our air, giving the impression that the CO2 is just destroyed in some way, and there is no suggestion that destroying forests can release that CO2 back into the air.
2. Trees absorb and store carbon dioxide - this is a slight improvement over number 1 in that it includes the idea that trees temporarily store carbon dioxide, which will then be released again when the tree dies or is destroyed. However, trees do not really store CO2, they convert it into the other carbon-based compounds they need to survive and grow (sugars, cellulose, lignin). In fact, while trees do absorb CO2 from the atmosphere through the pores in their leaves during the day, the opposite occurs at night, albeit to a lesser extent, as well as during the metabolism of sugars by plant cells, and when it sheds its leaves (however, even given all that, trees do remain a net absorber of carbon).
3. Forests are the lungs of the planet - the analogy with human or animal lungs is a little misplaced in that our lungs take in oxygen and expel other gases, including carbon dioxide, the opposite of what happens with plants and trees. But, as a metaphor, this model may be useful in that it emphasizes the idea of a gas exchange. But again, it suggests that the CO2 is essentially eliminated rather than stored or used by the plants. Also, it is NOT the case that trees provide all our oxygen, as is sometimes implied - if all our trees were killed, it would be an environmental catastrophe, but we would not suddenly find ourselves without oxygen. Cutting down a tree, or even a whole forest, does not suddenly release huge amounts of carbon dioxide into the atmosphere, as is sometimes claimed or implied. However, burning down a forest, e.g. for farming land, does release its carbon.
4. Green plants use sunlight to convert CO2 and water into sugar - this is all true as far as it goes, and an understanding of the process of photosynthesis is essential. It provides the reason why trees and other plants take CO2 out of the air in the first place: the sugars they manufacture from it serve as food and building materials, and they only give off oxygen as a coincidental waste product of that process. However, bear in mind that, while the tree is actually using the sugars in its cells, it is doing the exact opposite: taking in oxygen from the air and expelling CO2, as it also does at night. 
5. Green plants create biomass, while animals and decomposers break it down - although trees do use the sugars that they produce from the CO2 and water they take in to power their metabolic processes, the majority of it is actually used to produce cellulose and lignin (the "woody" parts of trees), for which other compounds like nitrogen are needed and obtained via the root system. This biomass therefore contains a lot of stored chemical energy (think firewood, coal, etc). But, yes, all plants are biomass, as are the undergroud roots and fallen leaf litter.
6. The forests of the world are a huge carbon sink - a "carbon sink" is anything that absorbs and stores carbon in one form or another, so the carbon-rich biomass of trees (particularly tropical trees, which store even more carbon  than temperate trees) does represent a significant carbon sink. However, when fallen leaves or dead trees decompose, or when they burn, they yield carbon dioxide back into the atmosphere. However, soils, particularly peatlands (which are prevented from decomposition by their acidity and moisture), as well as grasslands and mangrove swamps, are an even greater carbon sink: worldwide, there is more organic carbon stored in the top metre of soil than in all the above-ground biomass, including forests. Our fossil fuel reserves of oil, gas and coal are another such carbon sink, being just a buried source of compressed, undecomposed vegetation, so that when we burn it, we release stored carbon back to the air. Even limestone contains stored carbon, which releases CO2 to the atmosphere when we use it to make concrete, for example. And, given that carbon dioxide is water-soluble, the world's huge oceans are an even more important carbon sink than any of these land-based sinks.

A combination of the last three of these thought models is perhaps the best way of thinking of forests and their relationship with carbon and climate. But the complexity of the systems involved are a good indication of why the whole greenhouse gas/climate change issue is so fraught.