Sweaty feet (hyperhidrosis) ans Smelly feet (bromhidrosis)

The feet and hands contain more sweat glands than any other part of the body.
Smelly feet can be embarrassing and physically uncomfortable.

Feet smell for two reasons: 1) shoe wear, and 2) sweating of the feet.
The interaction between the perspiration and the bacteria that thrive in shoes and socks produce the odour. 
 
Bromhidrosis is a condition of abnormal or offensive body odour, to a large extent determined by apocrine gland secretion, although other sources may play a role.

Throughout the average day, the body naturally perspires to regulate heat in the body. In some individuals, natural perspiration is excessive in the feet which results in sweaty feet.
People are also more prone to foot perspiration if on their feet all day, if they are under a lot of stress or have a medical condition called hyperhidrosis - the name given to excessive and uncontrollable sweating.

Excessive sweating can be caused by an inherited condition, called hyperhidrosis.
Stress, some medications, fluid intake, and hormonal changes can also increase the amount of perspiration.

As there are more sweat glands in the feet than anywhere else in the body anyone can experience sweaty feet regardless of the temperature.