Our Stoic forefathers were materialists (but they were not atomists or corpuscular theorists like the Epicureans or many early modern natural philosophers such as Hobbes). They believed, for example, that two "bodies" could occupy the same place at the same time, and their pneuma, an active body composed of air and fire in varying proportions, was a force field that integrates or renders coherent those natural entities that have some unity or individuality.
I mention their dynamic materialism because it strongly suggests that you cannot totally wall off one part of the soul or person from another. In fact, at least Chrysippus, probably the greatest of the Stoic philosophers (the third head of Zeno's school) sharply disagreed with the psychology of Plato and Aristotle according to whom the soul itself is divided into rational and nonrational parts.
In the Plato-Aristotle theory, the rational part, known as the reason, or mind, or intellect, is supposed to rule the nonrational parts (also known as the passions). In Plato's version, the nonrational parts consist of the spirited part (with which we get angry or feel fear or confidence) and the appetitive part (with which we desire food, drink and generally physical pleasure, and possessions). In the virtuous person, according to this theory, the nonrational parts will be trained or habituated to follow the guidance of reason.
Chrysippus rejected this bi- or tripartite psychology: the soul is essentially a unity, he said, the cognitive or judgment-making part is thoroughly interwoven with the affective or feeling part, so that they are effectively one and the same. Passions are excessive feelings corresponding to false judgments. Actually, even that is too tame, and Aristotle might have agreed with it. Chrysippus' view is that passions *are* false judgments. For example, lust after money just *is* the (false) judgment that money is literally a good thing (that one might pursue at the expense of doing the morally right thing), as distinct from a merely "preferred" thing that one might prefer to have when the selection is merely between having it and not having it.
Incidentally, a contemporary philosopher who analyzes the emotions as judgments is Robert C. Solomon. His book The Passions (Hackett Publishers) is well worth studying.
Another aside: Larry Becker in A New Stoicism disagrees with Chrysippus on this question and takes up with Posidonius, who went back at least partly toward the Platonic-Aristotelian view on this question. Sometimes the dispute between the Stoics and the Aristotelians (or between Chrysippus and Posidonius within the Stoa) on this point is just a question of semantics. Even if we only insist that judgments and feelings are tightly correlated with one another, we undercut the popular false dichotomy between feeling and reason.
The issue is not logic good feeling bad, v. logic bad feeling good, as some would have it. It is whether one could give a reasonable account, all things considered, for the judgments one makes AND the feelings one has (since the two go hand in hand). The person who lusts for money or power and is sent into depression when her stock loses a few points is making judgments that have an insufficient rational basis as well as undergoing the [irrational] passions. On the other hand, the person whose life is well-integrated and is "making progress" towards sagedom, will presumably experience something like a smooth flow of life, with the appropriate feelings that this implies, as well as make fitting (rational) judgments about the values of things and how valuable they are.
Both Aristotle and the old Stoics understood that wisdom is not a matter of blending feeling with reason, as if the two were fluids (today we might say "energies") that could be isolated from one another but could also be mixed in various proportions. (One of the reasons that I am suspicious of psychologies inspired by Carl Jung is that his categories suggest that humans can be mostly emotional or mostly rational--the latter may not be his term; his terminology reinforces the popular dichotomies and fuzzy thinking about this issue.)
As for imagination and reason, the opposition between these two is based on some old charts, such as Plato's Divided Line, according to which imagination is the earliest and most primitive cognitive stage. This is symbolized in the Cave Allegory by the prisoners in the cave who see nothing but shadows on the cave wall and take them to be real. Rather like couch potatoes who take sitcoms for real or the nightly news as filtered through monopoly media corporations. Imagination in this sense is the inability to take as real anything but surface impressions.
Two things have to be said about this. First of all, we must be able to receive surface impressions (for in a sense we construct all we ever learn from them), and so even the mental stage Plato called imagination is in touch with partial reality. (Plato's vital point was that it is very partial.) Secondly, "imagination" as we now use the term is a far more exalted mental capacity, the capacity to conceive not only what is not present here and now, but perhaps what has never existed in any place or at any time. Imagination in this sense is the faculty that enables us to conceive possibilities that may or may not be true; without it there would be no progress in science or philosophy; in fact, without it, logic as a philosophical discipline could not have evolved.