**Core Concept**
Carotid body tumors are paragangliomas that arise from the paraganglia of the carotid body, a chemoreceptor organ located at the bifurcation of the common carotid artery. Resection of these tumors can lead to various complications due to their proximity to critical structures in the neck.

**Why the Correct Answer is Right**
The most frequent complication after resection of carotid body tumors is hypoglossal nerve palsy. This occurs due to the close proximity of the hypoglossal nerve to the carotid body and the potential for nerve injury during tumor dissection. The hypoglossal nerve is responsible for innervating the tongue and plays a crucial role in tongue movement and speech. Damage to this nerve can result in difficulty speaking and swallowing, as well as weakness or paralysis of the tongue.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because while hoarseness of voice is a possible complication of carotid body tumor resection, it is not the most frequent complication. Hoarseness is more commonly associated with injury to the recurrent laryngeal nerve.
**Option B:** This option is incorrect because while dysphagia (difficulty swallowing) can occur after carotid body tumor resection, it is not the most frequent complication. Dysphagia can result from injury to the vagus nerve or other structures in the neck.
**Option C:** This option is incorrect because while facial weakness is a possible complication of carotid body tumor resection due to injury to the facial nerve, it is not the most frequent complication. Facial weakness is more commonly associated with Bell's palsy or other conditions.

**Clinical Pearl / High-Yield Fact**
It's essential to note that the hypoglossal nerve can be at risk during carotid body tumor resection, and surgeons should take precautions to identify and preserve this nerve to minimize the risk of postoperative complications.

**Correct Answer:** D. Hypoglossal nerve palsy.