**Core Concept**
Fine-needle aspiration cytology (FNAC) is a crucial diagnostic tool for evaluating thyroid nodules, especially those with suspicious ultrasound characteristics or positive family history of thyroid cancer. The presence of a cold nodule on radionuclide scan and a non-cystic solid mass on ultrasound raises suspicion for malignancy.

**Why the Correct Answer is Right**
In this scenario, the patient's presentation warrants further investigation. The cold nodule on radionuclide scan indicates reduced or absent iodine uptake, which can be seen in both benign and malignant thyroid nodules. However, the ultrasound findings of a non-cystic solid mass are more concerning for malignancy. Fine-needle aspiration cytology (FNAC) is the next step in management, as it allows for the collection of cell samples for histopathological examination, helping to differentiate between benign and malignant lesions.

**Why Each Wrong Option is Incorrect**
**Option A:** Surgery is not the initial step, as FNAC is necessary to confirm the nature of the thyroid nodule before proceeding with surgical intervention.
**Option B:** Thyroid function tests (TFTs) are essential in evaluating thyroid nodules, but they are not the primary management strategy in this case, where the ultrasound and radionuclide scan suggest a higher likelihood of malignancy.
**Option C:** Hormone therapy is not indicated in the management of thyroid nodules, especially when there is suspicion of malignancy.

**Clinical Pearl / High-Yield Fact**
When evaluating thyroid nodules, it's essential to remember that a "cold" nodule on radionuclide scan does not necessarily indicate malignancy, but a non-cystic solid mass on ultrasound raises suspicion for malignancy, prompting further investigation with fine-needle aspiration cytology (FNAC).

**Correct Answer:** C. Fine-needle aspiration cytology (FNAC)