Yes a cold virus or any other viruses can be spread and transmitted through food.
If you have a cold virus and then touch food with your bare hands and serve the food to someone else and they eat that food that you touched without washing your hands then you can transmit that cold virus to the other person.
If you have a cold and need to prepare food for family you should make sure you wash your hands before handling the food and wear plastic food grade gloves to help prevent the spread of cold viruses.
I always wash my hands before cooking and handling food and wash my hands more often during cold and flu season.
Still people catch a cold virus but it does prevent the spread of cold viruses and other food borne illnesses when you wash your hands and the surfaces that you prepare food on.
Cold viruses can also be spread through coughing, touching other peoples hands such as shaking someone else's hands, doorknobs etc.
I wipe everything down that people touch during cold and flu season to help prevent the spread of the cold and flu viruses.