Edit: Is it because as the resistance on the venule end of the capillary increases, the venule's diameter grows smaller, so the hydrostatic pressure increases?
Yep, that's exactly right. When ever I approach these types of problems, two things come to mind: cardiac output and peripheral resistance (both which predetermine the mean arteriole pressure or MAP). Cardiac Output, because of it's relation to MAP, essentially is synonymous with pressure. It's the amount of blood pumped out of the heart per minute and is determined by: stroke volume (volume blood/heartbeat) x heart rate (heartbeats/minute). Peripheral resistance is also synonymous with pressure due to its relation to MAP. Increasing resistance, increases pressure and vice versa.
So, consider what happens during the activation of the sympathetic system. If you ever became nervous at some point in your life, which I'm sure you have, this should be familiar. On a physiological level, here's what happens. The sympathetic system innervates the arteries and releases a neurotransmitter (noradrenaline/adrenaline). For the arteries, this neurotransmitter acts on a specific adrenergic receptor (alpha 1). Stimulation of this receptor results in a cascade that depolarizes the smooth muscle of the cell, ultimately allowing calcium concentration to increase inside the smooth muscle cell. What do you suppose happens? Hopefully, you said muscle contraction. Muscle contraction of smooth muscle results in vasoconstriction.
So what does this mean and why is this important? On a physiological level, this increases the individuals blood pressure. But how is the question. Visualize this with a picture:
The constriction of the smooth muscle results in a build up of fluid or blood behind the point of constriction resulting in an increase of pressure. If it helps, think of what happens if you compress a garden hose. You could probably feel the resistance and increase of pressure building up. But what also happens? A bunch of water squirts out right? So while pressure increases directly due to constriction, it also increases due to increase venous return. Venous return, by increasing the amount of blood to the heart, allow it to contract more forcefully, pumping out more blood.... increasing more pressure (build up of fluid beyond the constriction point). Refer to the equation above to see how this effects cardiac output (which indirectly increases pressure). Therefore, increasing venous return will also increase blood pressure. There are also several other things to consider. The nodes of the heart beat are innervated by the automatic nervous system. Sympathetic stimulation will also allow the SA nodes to fire more frequently (how? Adrenaline acts on the B1 adrenergic receptor of the heart, a metabotropic receptor which increases cAMP production, stimulating the "funny ion" channel, which is responible for spontaneous depolarization; increased activity of funny ion channel, more firing of SA, increased heart rate). As you can see, it can be very complex, but if you understand the basics, everything else will fall through. Hope this helps.
Here's a few other interesting things to mention: If you ever encountered an individual who, for whatever reason is having an allergic reaction and is undergoing anaphylactic shock (due to release of TNF-alpha, resulting in increase blood permeability and vasodialation (due to histamine), loss of blood plasma, and as a result, a dramatic decrease in blood pressure), these individuals must immediately be given an "epi shot" aka a shot of adrenaline. Considering everything mentioned above, this should make sense why this is beneficial for this individual. If not treated immediately, this person will die of heart failure due to a huge decline in blood pressure. The epi shot reverses this.
Also consider on the opposite spectrum what happens if you gave an asthma patient a beta blocker. Above I mentioned one beta receptor, for the heart (B1). But there are others, including B2 of the lungs. Binding of adrenaline to B2 results in bronchodialation. (Another consequence of the "Fight of Flight" response; allows increase oxygen into body). A non-selective beta inhibitor would block beta receptors, thereby reducing all the effects typical of adrenaline. By blocking adrenaline input, as a consequence (among other effects), the individual experiences bronchoconstriction. This is catastrophic for an asthma patient and would kill them ...something to keep in mind for the future.