Hearing loss especially when associated with pain can be quite distressing and should be evaluated by your primary care physician
as soon as possible. After your initial evaluation, he or she may decide to refer you to an ENT doctor
that specializes in ear function. The answer to your question is probably not. Cold temperatures are not typically associated with ruptured tympanic membranes (ear drums). That is not to say that it could not happen, but you would probably have to have something wrong with your eardrum prior to the incident for cold weather to do that. Tympanic membrane rupture is almost always caused by either physical trauma (sticking something in your ear and breaking the membrane) or barotrauma. Barotrauma occurs when patient's have a membrane rupture either when flying or scuba diving when pressures around their ears change. Therefore it is more likely that the sharp pain in your ear along with the subsequent hearing loss is due to something else. You may have a waxy obstruction or a middle ear infection
that needs to be treated. There are definitely more possibilities that can be listed here. I think it would be wise to get your ears looked at as soon as possible. Good luck.