Tree census data for Sweden/Scandinavia?
I would definatley look at data from Swedish National Forest Inventory (Riksskogstaxeringen). They have time series data of multiple variables (DBH, size classes, species, dead wood etc) from plots all over the country. Extrapolations based on these data should produce reasonable estimates of total tree count, and probably the most accurate one that can be obtained at the moment. As an example, this report (in swedish) includes graphs on trees/km$^2$ for different species and areas (page 17 ff), but this is only based on areas that can support productive forestry.