Is wearing mouth retainer an effective way to stop snoring?

No: A traditional mouth guard is not designed for snoring you would need a snore guard or other sleep device which is specifically designed for snoring.

It can be: If you are a robust snorer, you should first have a sleep study to make sure you don't have sleep apnea. If not, an appliance made by a dentist who is trained in this procedure, is a viable alternative.

Terminology: Both retainers and snoring reduction appliances are removable, but not exactly the same thing. Retainers hold teeth stable after tooth movement. Snoring reduction appliances position lower jay forward during sleep to open the airway. See your dentist or an orthodontist for support.

Not necessarily: Unless your retainer opens your airway or repositions your jaw, it is unlikely to help, talk to your dentist or medical doctor for ideas.