A wool scarf can keep you warmer than a synthetic scarf for several reasons:

 

Insulation: Wool fibres naturally trap warm air, providing insulation to keep you warm. Synthetic fibres do not have the same insulating properties.

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Moisture-wicking: Wool fibres have a natural ability to absorb and wick away moisture, which helps to keep you dry and warm. Synthetic fibres do not have this ability, and can become clammy and uncomfortable when they come in contact with sweat or humidity.

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Warmth-to-weight ratio: Wool has a high warmth-to-weight ratio, meaning it provides a lot of warmth for its weight. This makes it a popular choice for outdoor and cold-weather clothing, as it is lightweight and easy to pack, but still provides excellent insulation. Synthetic fibres often do not provide the same level of warmth for their weight.

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Durability: Wool fibres are naturally strong and resilient, and can withstand a lot of wear and tear without breaking down. Synthetic fibres are often less durable and may wear out more quickly.

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Natural vs Synthetic: Wool is natural and biodegradable, while synthetic fibres are man-made and can take hundreds of years to degrade.