Why is it that we don't drink medicine with very cold water

Medicines are absorbed across biological membranes in stomach and intestines. For this to be effective, there has be optimal concentration of dissolved drug and an optimal temperature in the lumen(cavity) of the stomach and intestines.

Cold water reduces both the capacity of drug to dissolve/ disperse as well as creates a suboptimal temperature for absorption, thus decreasing the amount of drug absorbed into the system.

Medicines are the best taken dispersed, like in syrup or suspension form. But they are commonly dispensed in tablet form for convenience of storage and improved shelf life. Generally medicines would act better and faster if taken crushed/ dispersed along with warm water.