I do not understand exactly what is meant by node size. I know what a decision node is, but not what node size is.
A decision tree works by recursive partition of the training set. Every node $t$ of a decision tree is associated with a set of $n_t$ data points from the training set:
You might find the parameter
nodesize in some random forests packages, e.g. R: This is the minimum node size, in the example above the minimum node size is 10. This parameter implicitly sets the depth of your trees.
nodesize from R random forest package
Minimum size of terminal nodes. Setting this number larger causes smaller trees to be grown (and thus take less time). Note that the default values are different for classification (1) and regression (5).
In other packages you directly find the parameter
depth, e.g. WEKA:
-depth from WEKA random forest package
The maximum depth of the trees, 0 for unlimited. (default 0)
It is not clear if the nodesize is on the "in-bag" sampling or on the "out-of-bag" error. If it is on the "out-of-bag" sampling, it is slightly more restrictive.