My gums and/or teeth bottom left side have been hurting when i drink or eat something cold. i want to know why?

The cause of your: Dental problems cannot be determined over the internet. That would require a clinical exam and x-rays. There are too many possibilities to even list. See a local dentist to determine the cause of your discomfort and what would be the appropriate treatment.

Could be a cavity..: .. Or a cracked filling, or a fractured tooth, or gum recession. So hard to know for sure without seeing it together with a radiograph. Make an appointment with a local dentist to find out the cause and what treatment may be indicated.

Many possibilities: Sensitivity to temperature could be simple root exposure/gum recession and resultant "dentin hypersensitivity." unfortunately, cold sensitivity can also be from decay, a defective filling, a crack/fracture of the tooth, or trauma from a tooth or filling that interferes with the bite. Best to have it evaluated by your dentist.

Cavity?: Could be a cavity or gum recession which exposes the tooth nerve which reacts with a pain sensation. See your dentist.